{"id":9268,"date":"2025-10-17T20:15:46","date_gmt":"2025-10-17T11:15:46","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?page_id=9268"},"modified":"2026-09-27T12:20:40","modified_gmt":"2026-09-27T03:20:40","slug":"ch11-formal-logic","status":"publish","type":"page","link":"https:\/\/sasamath.com\/blog\/invitation-to-mathematical-logic\/ch11-formal-logic\/","title":{"rendered":"\ud615\uc2dd\ub17c\ub9ac"},"content":{"rendered":"<div class=\"mathlogic2025\"><!-- ################## --><\/p>\n<p><a href=\"\/blog\/invitation-to-mathematical-logic\/ch01-naive-logic\/\">1\uc7a5<\/a>\uc5d0\uc11c\ub294 \uba85\uc81c\uc640 \ub17c\ub9ac \uc5f0\uc0b0, \ucd94\ub860 \uaddc\uce59\uc744 \uc9c1\uad00\uc801\uc778 \uc218\uc900\uc5d0\uc11c \ub2e4\ub8e8\uc5c8\ub2e4. \uc218\ud559\uc801 \ucd94\ub860\uc744 \uc5c4\ubc00\ud558\uac8c \ubd84\uc11d\ud558\uace0 \uba85\ub8cc\ud55c \uc808\ucc28\uc5d0 \ub530\ub77c \uac80\uc99d\ud558\ub824\uba74 \uc774\ub7ec\ud55c \ub17c\ub9ac\ub97c \ud615\uc2dd\uc801 \uae30\ud638 \uccb4\uacc4\ub85c \ud45c\ud604\ud560 \ud544\uc694\uac00 \uc788\ub2e4. \ud615\uc2dd\ub17c\ub9ac\ub294 \uc77c\uc0c1 \uc5b8\uc5b4\uc758 \ubaa8\ud638\ud568\uc744 \uc904\uc774\uace0 \uba85\ud655\ud55c \uad6c\ubb38 \uaddc\uce59\uacfc \ucd94\ub860 \uaddc\uce59\uc5d0 \ub530\ub77c \ub17c\ub9ac\uc801 \ucd94\ub860\uc744 \uc804\uac1c\ud558\uac8c \ud574 \uc8fc\ub294 \uccb4\uacc4\uc774\ub2e4.<\/p>\n<p>\uc218\ud559\uc5d0\uc11c \uc8fc\ub85c \uc0ac\uc6a9\ud558\ub294 \ud615\uc2dd\ub17c\ub9ac\ub294 \ud06c\uac8c \uba85\uc81c\ub17c\ub9ac\uc640 \uc77c\uacc4\ub17c\ub9ac\uac00 \uc788\ub2e4. \uba85\uc81c\ub17c\ub9ac\ub294 \uba85\uc81c\ub4e4 \uc0ac\uc774\uc758 \ub17c\ub9ac\uc801 \uad00\uacc4\ub97c \ub2e4\ub8e8\ub294 \uac00\uc7a5 \uae30\ubcf8\uc801\uc778 \ub17c\ub9ac \uccb4\uacc4\uc774\uba70, \uc77c\uacc4\ub17c\ub9ac\ub294 \uc5ec\uae30\uc5d0 \ud55c\uc815\uae30\ud638\uc640 \uad00\uacc4, \ud568\uc218 \ub4f1\uc744 \ucd94\uac00\ud558\uc5ec \uc218\ud559\uc758 \ub9ce\uc740 \ub0b4\uc6a9\uc744 \ud45c\ud604\ud560 \uc218 \uc788\uac8c \ud655\uc7a5\ud55c \uccb4\uacc4\uc774\ub2e4. \uc774\ub4e4 \ub17c\ub9ac \uccb4\uacc4\uc5d0\uc11c\ub294 \uad6c\ubb38\ub860\uc801 \uad00\uc810(\ud615\uc2dd\uc801 \uc99d\uba85)\uacfc \uc758\ubbf8\ub860\uc801 \uad00\uc810(\uc9c4\ub9bf\uac12\uacfc \ubaa8\ub378) \uc0ac\uc774\uc758 \uad00\uacc4\uac00 \ud575\uc2ec\uc801\uc778 \uc8fc\uc81c\uac00 \ub41c\ub2e4.<\/p>\n<p>\uc774 \ubd80\uc5d0\uc11c\ub294 \ud615\uc2dd\ub17c\ub9ac\uc758 \uae30\ubcf8 \uac1c\ub150\ubd80\ud130 \uc2dc\uc791\ud558\uc5ec \uba85\uc81c\ub17c\ub9ac\uc640 \uc77c\uacc4\ub17c\ub9ac\uc758 \uad6c\ubb38\ub860\uacfc \uc758\ubbf8\ub860\uc744 \uc0b4\ud3b4\ubcf8\ub2e4. \ud2b9\ud788 \uac74\uc804\uc131\uacfc \uc644\uc804\uc131 \uc815\ub9ac\ub97c \ud1b5\ud574 \ud615\uc2dd\uc801 \uc99d\uba85\uacfc \uc758\ubbf8\ub860\uc801 \ud0c0\ub2f9\uc131\uc758 \uad00\uacc4\ub97c \ud655\uc778\ud558\uace0, \uc774\uac83\uc774 \uc218\ud559\uc758 \uae30\ucd08\uc5d0\uc11c \uc5b4\ub5a4 \uc758\ubbf8\ub97c \uac16\ub294\uc9c0 \uc0b4\ud3b4\ubcf8\ub2e4.<\/p>\n<p><!-- \n\n<h2>11. \ud615\uc2dd\ub17c\ub9ac\uc758 \uac1c\ub150<\/h2>\n\n --><\/p>\n<h3>\ud615\uc2dd\ub17c\ub9ac\uc758 \uac1c\ub150<\/h3>\n<p>\ud615\uc2dd\ub17c\ub9ac\ub294 \uc218\ud559\uc801 \ucd94\ub860\uc5d0\uc11c \uc0ac\uc6a9\ud558\ub294 \uae30\ud638\uc640 \uc2dd, \uacf5\ub9ac, \ucd94\ub860 \uaddc\uce59\uc744 \uba85\uc2dc\ud558\uc5ec \uc99d\uba85\uc744 \uc720\ud55c\ud55c \uae30\ud638 \uc870\uc791\uc73c\ub85c \ub2e4\ub8f0 \uc218 \uc788\uac8c \ud558\ub294 \uccb4\uacc4\uc774\ub2e4. \uc774 \uc808\uc5d0\uc11c\ub294 \u201c\ud615\uc2dd\uc801\uc73c\ub85c \uac80\uc0ac\ud560 \uc218 \uc788\ub3c4\ub85d\u201d <span class=\"defined\">\ud6a8\uacfc\uc801\uc73c\ub85c \uc81c\uc2dc<\/span>\ub41c \ud615\uc2dd\uacc4\ub97c \uc0dd\uac01\ud55c\ub2e4.<\/p>\n<div class=\"box theorem\">\n<p><span class=\"definition\">\uc815\uc758 11.1. (\ud615\uc2dd\uacc4)<\/span><\/p>\n<p><span class=\"defined\">\ud615\uc2dd\uacc4<\/span>(formal system)\ub294 \ub2e4\uc74c \uc790\ub8cc\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uccb4\uacc4\uc774\ub2e4.<\/p>\n<ul>\n<li><span class=\"defined\">\uc54c\ud30c\ubcb3<\/span>(alphabet): \uc2dd\uc744 \ub9cc\ub4dc\ub294 \ub370 \uc0ac\uc6a9\ud558\ub294 \uae30\ud638\ub4e4\uc758 \uc9d1\ud569\uc774\ub2e4.<\/li>\n<li><span class=\"defined\">\ub17c\ub9ac\uc2dd<\/span>(formula)\uc758 \uc9d1\ud569: \uc54c\ud30c\ubcb3\uc758 \uae30\ud638\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uc720\ud55c\ud55c \ubb38\uc790\uc5f4 \uac00\uc6b4\ub370 \ubb38\ubc95 \uaddc\uce59\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \uac83\ub4e4\uc758 \uc9d1\ud569\uc774\ub2e4. \uc8fc\uc5b4\uc9c4 \ubb38\uc790\uc5f4\uc774 \ub17c\ub9ac\uc2dd\uc778\uc9c0 \ud615\uc2dd\uc801\uc73c\ub85c \ud310\ubcc4\ud560 \uc218 \uc788\uc5b4\uc57c \ud55c\ub2e4.<\/li>\n<li><span class=\"defined\">\uacf5\ub9ac<\/span>(axiom)\uc758 \uc9d1\ud569: \uc99d\uba85 \uc5c6\uc774 \ucd9c\ubc1c\uc810\uc73c\ub85c \ud5c8\uc6a9\ud558\ub294 \ub17c\ub9ac\uc2dd\ub4e4\uc758 \uc9d1\ud569\uc774\ub2e4. \uc5ec\uae30\uc11c\ub294 \uc8fc\uc5b4\uc9c4 \ub17c\ub9ac\uc2dd\uc774 \uacf5\ub9ac\uc778\uc9c0 \ud615\uc2dd\uc801\uc73c\ub85c \ud310\ubcc4\ud560 \uc218 \uc788\ub2e4\uace0 \uac00\uc815\ud55c\ub2e4.<\/li>\n<li><span class=\"defined\">\ucd94\ub860 \uaddc\uce59<\/span>(rule of inference): \uc720\ud55c \uac1c\uc758 \ub17c\ub9ac\uc2dd\uc744 \uc804\uc81c\ub85c \ud558\uc5ec \uc0c8\ub85c\uc6b4 \ub17c\ub9ac\uc2dd\uc744 \uacb0\ub860\uc73c\ub85c \uc5bb\ub294 \uaddc\uce59\uc774\ub2e4. \uc8fc\uc5b4\uc9c4 \ud55c \ub2e8\uacc4\uac00 \ucd94\ub860 \uaddc\uce59\uc758 \uc62c\ubc14\ub978 \uc801\uc6a9\uc778\uc9c0 \ud615\uc2dd\uc801\uc73c\ub85c \ud310\ubcc4\ud560 \uc218 \uc788\uc5b4\uc57c \ud55c\ub2e4.<\/li>\n<\/ul>\n<\/div>\n<div class=\"box theorem\">\n<p><span class=\"definition\">\uc815\uc758 11.2. (\uc99d\uba85\uacfc \uc815\ub9ac)<\/span><\/p>\n<p>\ud615\uc2dd\uacc4\uc5d0\uc11c <span class=\"defined\">\uc99d\uba85<\/span>(proof)\uc774\ub780 \ub17c\ub9ac\uc2dd\uc758 \uc720\ud55c\ud55c \uc5f4<br \/>\n\\[<br \/>\n\\varphi_1,\\,\\varphi_2,\\,\\ldots,\\,\\varphi_n<br \/>\n\\]<br \/>\n\uc73c\ub85c\uc11c, \uac01 \\(\\varphi_i\\)\uac00 \uacf5\ub9ac\uc774\uac70\ub098 \uc55e\uc5d0 \ub098\ud0c0\ub09c \ub17c\ub9ac\uc2dd\ub4e4\uc5d0 \ucd94\ub860 \uaddc\uce59\uc744 \uc801\uc6a9\ud558\uc5ec \uc5bb\uc5b4\uc9c4 \uac83\uc744 \ub9d0\ud55c\ub2e4. \uc5b4\ub5a4 \ub17c\ub9ac\uc2dd\uc774 \uc5b4\ub5a4 \uc99d\uba85\uc758 \ub9c8\uc9c0\ub9c9 \ub17c\ub9ac\uc2dd\uc73c\ub85c \ub098\ud0c0\ub098\uba74 \uadf8 \ub17c\ub9ac\uc2dd\uc744 \uadf8 \ud615\uc2dd\uacc4\uc758 <span class=\"defined\">\uc815\ub9ac<\/span>(theorem)\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n<\/div>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 11.1.<\/span><br \/>\n\ub17c\ub9ac\uc2dd\uc774 \\(\\varphi_n\\;(n\\in\\mathbb N)\\)\uc774\uace0, \uc720\uc77c\ud55c \uacf5\ub9ac\uac00 \\(\\varphi_0\\)\uc774\uba70, \uc720\uc77c\ud55c \ucd94\ub860 \uaddc\uce59\uc774<br \/>\n\\[<br \/>\n\\frac{\\varphi_n}{\\varphi_{n+1}}<br \/>\n\\]<br \/>\n\uc778 \ud615\uc2dd\uacc4 \\(\\mathcal F\\)\ub97c \uc0dd\uac01\ud558\uc790. \uc704\uc640 \uac19\uc740 \ud45c\uae30\ub294 \u201c\\(\\varphi_n\\)\uc73c\ub85c\ubd80\ud130 \\(\\varphi_{n+1}\\)\uc744 \ucd94\ub860\ud55c\ub2e4\u201d\ub77c\ub294 \ub73b\uc774\ub2e4. \ub2e4\uc74c \uc720\ud55c\ud55c \ub17c\ub9ac\uc2dd\uc758 \uc5f4\uc774 \\(\\mathcal F\\)\uc758 \uc99d\uba85\uc778\uc9c0 \ud310\uc815\ud558\uc2dc\uc624. \uc99d\uba85\uc774\ub77c\uba74 \ub9c8\uc9c0\ub9c9 \ub17c\ub9ac\uc2dd\uc774 \uc5b4\ub5a4 \uc815\ub9ac\uc778\uc9c0\ub3c4 \uc4f0\uc2dc\uc624.<\/p>\n<ol class=\"parenthesis\">\n<li>\\(\\varphi_0\\)<\/li>\n<li>\\(\\varphi_0,\\varphi_1,\\varphi_2,\\varphi_3\\)<\/li>\n<li>\\(\\varphi_0,\\varphi_2\\)<\/li>\n<li>\\(\\varphi_1,\\varphi_2\\)<\/li>\n<li>\\(\\varphi_0,\\varphi_1,\\varphi_1,\\varphi_2\\)<\/li>\n<\/ol>\n<\/div>\n<p>\uc774\ucc98\ub7fc \ud6a8\uacfc\uc801\uc73c\ub85c \uc8fc\uc5b4\uc9c4 \ud615\uc2dd\uacc4\uc5d0\uc11c\ub294 \uc8fc\uc5b4\uc9c4 \uc720\ud55c\ud55c \ub17c\ub9ac\uc2dd\uc758 \uc5f4\uc774 \uc62c\ubc14\ub978 \uc99d\uba85\uc778\uc9c0 \uac80\uc0ac\ud560 \uc218 \uc788\ub2e4. \ub530\ub77c\uc11c \uac00\ub2a5\ud55c \uc720\ud55c\ud55c \ubb38\uc790\uc5f4\ub4e4\uc744 \ucc28\ub840\ub85c \uc870\uc0ac\ud568\uc73c\ub85c\uc368 \uc815\ub9ac\ub4e4\uc744 \uccb4\uacc4\uc801\uc73c\ub85c \uc5f4\uac70\ud560 \uc218 \uc788\ub2e4. \uadf8\ub7ec\ub098 \uc8fc\uc5b4\uc9c4 \ub17c\ub9ac\uc2dd\uc774 \uc815\ub9ac\uc778\uc9c0 \uc544\ub2cc\uc9c0\ub97c \ud56d\uc0c1 \uc720\ud55c\ud55c \uc2dc\uac04 \uc548\uc5d0 \ud310\ubcc4\ud560 \uc218 \uc788\ub294\uc9c0\ub294 \ubcc4\uac1c\uc758 \ubb38\uc81c\uc774\ub2e4. \uc774\ub7ec\ud55c \ud310\ubcc4 \uc808\ucc28\uac00 \uc874\uc7ac\ud558\ub294 \uc131\uc9c8\uc744 \u201c<span class=\"defined\">\uacb0\uc815\uac00\ub2a5<\/span>\ud558\ub2e4(decidable)\u201d\ub77c\uace0 \ud45c\ud604\ud55c\ub2e4. \uc815\ub9ac \uc5ec\ubd80\uac00 \uacb0\uc815\uac00\ub2a5\ud55c \ud615\uc2dd\uacc4\ub3c4 \uc788\uace0 \uadf8\ub807\uc9c0 \uc54a\uc740 \ud615\uc2dd\uacc4\ub3c4 \uc788\ub2e4.<\/p>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 11.2.<\/span><br \/>\n\ud6a8\uacfc\uc801\uc73c\ub85c \uc8fc\uc5b4\uc9c4 \ud615\uc2dd\uacc4\uc5d0 \uad00\ud55c \ub2e4\uc74c \uba85\uc81c\uc758 \ucc38\uacfc \uac70\uc9d3\uc744 \ud310\uc815\ud558\uace0 \uc774\uc720\ub97c \uc124\uba85\ud558\uc2dc\uc624.<\/p>\n<ol class=\"parenthesis\">\n<li>\uc8fc\uc5b4\uc9c4 \uc720\ud55c\ud55c \ub17c\ub9ac\uc2dd\uc758 \uc5f4\uc774 \uc62c\ubc14\ub978 \uc99d\uba85\uc778\uc9c0 \uc5ec\ubd80\ub294 \uc720\ud55c\ud55c \uc808\ucc28\ub85c \uac80\uc0ac\ud560 \uc218 \uc788\ub2e4.<\/li>\n<li>\ud615\uc2dd\uacc4\uc758 \uc815\ub9ac\ub4e4\uc744 \ud558\ub098\uc529 \uccb4\uacc4\uc801\uc73c\ub85c \uc5f4\uac70\ud560 \uc218 \uc788\ub2e4.<\/li>\n<li>\uc815\ub9ac\ub4e4\uc744 \uc5f4\uac70\ud560 \uc218 \uc788\uc73c\uba74, \uc784\uc758\uc758 \ub17c\ub9ac\uc2dd\uc774 \uc815\ub9ac\uc778\uc9c0 \uc5ec\ubd80\ub3c4 \ud56d\uc0c1 \uc720\ud55c\ud55c \uc2dc\uac04 \uc548\uc5d0 \ud310\uc815\ud560 \uc218 \uc788\ub2e4.<\/li>\n<li>\uc5b4\ub5a4 \ub17c\ub9ac\uc2dd\uc774 \uc815\ub9ac\uc758 \uc5f4\uac70 \uacfc\uc815\uc5d0\uc11c \ucc98\uc74c \\(N\\)\ub2e8\uacc4\uae4c\uc9c0 \ub098\ud0c0\ub098\uc9c0 \uc54a\uc558\ub2e4\uba74 \uadf8 \ub17c\ub9ac\uc2dd\uc740 \uc815\ub9ac\uac00 \uc544\ub2c8\ub2e4.<\/li>\n<\/ol>\n<\/div>\n<div class=\"box theorem\">\n<p><span class=\"definition\">\uc815\uc758 11.3. (\uba54\ud0c0\uc815\ub9ac)<\/span><\/p>\n<p>\ud615\uc2dd\uacc4 \uc790\uccb4\ub97c \uc218\ud559\uc801 \ub300\uc0c1\uc73c\ub85c \uc0bc\uc544 \uadf8 \uccb4\uacc4\uc758 \uc99d\uba85, \uc815\ub9ac, \uacb0\uc815\uac00\ub2a5\uc131 \ub4f1\uc758 \uc131\uc9c8\uc5d0 \uad00\ud558\uc5ec \uc5bb\ub294 \uc815\ub9ac\ub97c <span class=\"defined\">\uba54\ud0c0\uc815\ub9ac<\/span>(metatheorem)\ub77c\uace0 \ud55c\ub2e4. [\ucd08\uc218\ud559\uc801 \uc815\ub9ac\ub77c\uace0\ub3c4 \ubd80\ub978\ub2e4.] \uba54\ud0c0\uc815\ub9ac\ub294 \uc8fc\uc5b4\uc9c4 \ud615\uc2dd\uacc4 \uc548\uc5d0\uc11c \uc99d\uba85\ub418\ub294 \uc815\ub9ac\uc640 \uad6c\ubcc4\ub418\ub294, \uadf8 \ud615\uc2dd\uacc4\uc5d0 \uad00\ud55c \uc218\ud559\uc801 \uc9c4\uc220\uc774\ub2e4.<\/p>\n<\/div>\n<p>\ud615\uc2dd\uacc4\uc758 \uac04\ub2e8\ud55c \uc608\ub85c \ud638\ud504\uc2a4\ud0dc\ud130\uc758 <span class=\"defined\">MU-\uacc4<\/span>(MU-system)\ub97c \uc0b4\ud3b4\ubcf4\uc790.<\/p>\n<p>MU-\uacc4\uc758 \uc54c\ud30c\ubcb3\uc740 \\(\\{\\mathrm{M},\\mathrm{I},\\mathrm{U}\\}\\)\uc774\uba70, \uc774 \uc138 \uae30\ud638\ub85c \uc774\ub8e8\uc5b4\uc9c4 \ube44\uc5b4 \uc788\uc9c0 \uc54a\uc740 \ubaa8\ub4e0 \ubb38\uc790\uc5f4\uc744 \ub17c\ub9ac\uc2dd\uc73c\ub85c \uc0bc\ub294\ub2e4. \uacf5\ub9ac\ub294 \ud558\ub098\ubfd0\uc774\ub2e4.<br \/>\n\\[<br \/>\n\\mathrm{MI}<br \/>\n\\]<br \/>\n\ucd94\ub860 \uaddc\uce59\uc740 \ub2e4\uc74c \ub124 \uac00\uc9c0\uc774\ub2e4.<\/p>\n<ul>\n<li>\uaddc\uce59 1. \\(\\mathrm{I}\\)\ub85c \ub05d\ub098\ub294 \ubb38\uc790\uc5f4\uc758 \ub05d\uc5d0 \\(\\mathrm{U}\\)\ub97c \ucd94\uac00\ud560 \uc218 \uc788\ub2e4.<\/li>\n<li>\uaddc\uce59 2. \\(\\mathrm{M}x\\) \uaf34\uc758 \ubb38\uc790\uc5f4\uc5d0\uc11c \\(\\mathrm{M}\\) \ub4a4\uc5d0 \uc774\uc5b4\uc9c0\ub294 \ubb38\uc790\uc5f4 \\(x\\)\ub97c \ubcf5\uc81c\ud558\uc5ec \\(\\mathrm{M}xx\\)\ub97c \uc5bb\uc744 \uc218 \uc788\ub2e4.<\/li>\n<li>\uaddc\uce59 3. \ubb38\uc790\uc5f4\uc5d0 \\(\\mathrm{I}\\) \uc138 \uac1c\uac00 \uc5f0\ub2ec\uc544 \ub098\ud0c0\ub098\uba74 \uadf8 \uc138 \ubb38\uc790\ub97c \\(\\mathrm{U}\\) \ud558\ub098\ub85c \ubc14\uafc0 \uc218 \uc788\ub2e4.<\/li>\n<li>\uaddc\uce59 4. \ubb38\uc790\uc5f4\uc5d0 \\(\\mathrm{U}\\) \ub450 \uac1c\uac00 \uc5f0\ub2ec\uc544 \ub098\ud0c0\ub098\uba74 \uadf8 \ub450 \ubb38\uc790\ub97c \uc5c6\uc568 \uc218 \uc788\ub2e4.<\/li>\n<\/ul>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 11.3.<\/span><br \/>\nMU-\uacc4\uc758 \ucd94\ub860 \uaddc\uce59\uc744 \uc9c1\uc811 \uc801\uc6a9\ud558\uc5ec \ub2e4\uc74c \ubb3c\uc74c\uc5d0 \ub2f5\ud558\uc2dc\uc624.<\/p>\n<ol class=\"parenthesis\">\n<li>\\(\\mathrm{MI}\\)\uc5d0\uc11c \ucd94\ub860 \uaddc\uce59\uc744 \ud55c \ubc88 \uc801\uc6a9\ud558\uc5ec \uc5bb\uc744 \uc218 \uc788\ub294 \ubaa8\ub4e0 \ubb38\uc790\uc5f4\uc744 \uad6c\ud558\uc2dc\uc624.<\/li>\n<li>\\(\\mathrm{MIII}\\)\uc5d0\uc11c \ucd94\ub860 \uaddc\uce59\uc744 \ud55c \ubc88 \uc801\uc6a9\ud558\uc5ec \uc5bb\uc744 \uc218 \uc788\ub294 \ubaa8\ub4e0 \ubb38\uc790\uc5f4\uc744 \uad6c\ud558\uc2dc\uc624.<\/li>\n<li>\ub2e4\uc74c \uac01 \ubcc0\ud658\uc774 \ucd94\ub860 \uaddc\uce59\uc744 \ud55c \ubc88 \uc801\uc6a9\ud558\ub294 \uac83\uc778\uc9c0 \ud310\uc815\ud558\uace0, \ub9de\uc73c\uba74 \uc0ac\uc6a9\ud55c \uaddc\uce59\uc758 \ubc88\ud638\ub97c \uc4f0\uc2dc\uc624.<br \/>\n\\[<br \/>\n\\mathrm{MII}\\to\\mathrm{MIIU},\\quad<br \/>\n\\mathrm{MII}\\to\\mathrm{MIIII},\\quad<br \/>\n\\mathrm{MIIII}\\to\\mathrm{MUI},\\quad<br \/>\n\\mathrm{MUU}\\to\\mathrm{M},\\quad<br \/>\n\\mathrm{MUI}\\to\\mathrm{MUII}.<br \/>\n\\]<\/li>\n<\/ol>\n<\/div>\n<p>MU-\uacc4\uc5d0\uc11c\uc758 \uc99d\uba85\uc758 \uc608\ub294 \ub2e4\uc74c\uacfc \uac19\ub2e4.<br \/>\n\\[<br \/>\n\\mathrm{MI}<br \/>\n\\longrightarrow \\mathrm{MII}<br \/>\n\\longrightarrow \\mathrm{MIIII}<br \/>\n\\longrightarrow \\mathrm{MUI}<br \/>\n\\longrightarrow \\mathrm{MUIU}.<br \/>\n\\]<br \/>\n\ucc28\ub840\ub85c \uaddc\uce59 2, \uaddc\uce59 2, \uaddc\uce59 3, \uaddc\uce59 1\uc744 \uc801\uc6a9\ud55c \uac83\uc774\ub2e4.<\/p>\n<p>\uacf5\ub9ac\uc5d0\ub294 \\(\\mathrm{M}\\)\uc774 \ub9e8 \uc55e\uc5d0 \uc815\ud655\ud788 \ud55c \ubc88 \ub098\ud0c0\ub098\uace0, \uc5b4\ub290 \ucd94\ub860 \uaddc\uce59\ub3c4 \uc0c8\ub85c\uc6b4 \\(\\mathrm{M}\\)\uc744 \ub9cc\ub4e4\uac70\ub098 \uadf8 \uc704\uce58\ub97c \ubc14\uafb8\uc9c0 \uc54a\ub294\ub2e4. \ub530\ub77c\uc11c MU-\uacc4\uc758 \ubaa8\ub4e0 \uc815\ub9ac\ub294 \\(\\mathrm{M}x\\) \uaf34\uc774\uba70, \uc5ec\uae30\uc11c \\(x\\)\uc5d0\ub294 \\(\\mathrm{I}\\)\uc640 \\(\\mathrm{U}\\)\ub9cc \ub098\ud0c0\ub09c\ub2e4.<\/p>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 11.4.<\/span><br \/>\n\ub2e4\uc74c \uac01\uac01\uc774 MU-\uacc4 \ub0b4\ubd80\uc758 \ub17c\ub9ac\uc2dd \uc790\uccb4\uc778\uc9c0, \uc544\ub2c8\uba74 MU-\uacc4\uc5d0 \uad00\ud55c \uba54\ud0c0 \uc218\uc900\uc758 \uc9c4\uc220\uc778\uc9c0 \uad6c\ubcc4\ud558\uc2dc\uc624. \ub17c\ub9ac\uc2dd \uc790\uccb4\uc778 \uacbd\uc6b0\uc5d0\ub294 \uc9c0\uae08\uae4c\uc9c0 \uc81c\uc2dc\ub41c \uc99d\uba85\uc774\ub098 \uacf5\ub9ac\ub97c \uc774\uc6a9\ud558\uc5ec \uc815\ub9ac\uc778\uc9c0\ub3c4 \ud310\uc815\ud558\uc2dc\uc624.<\/p>\n<ol class=\"parenthesis\">\n<li>\\(\\mathrm{MI}\\)<\/li>\n<li>\\(\\mathrm{MUIU}\\)<\/li>\n<li>\u201cMU-\uacc4\uc758 \ubaa8\ub4e0 \uc815\ub9ac\ub294 \\(\\mathrm{M}\\)\uc73c\ub85c \uc2dc\uc791\ud55c\ub2e4.\u201d<\/li>\n<li>\u201c\\(\\mathrm{MU}\\)\ub294 MU-\uacc4\uc758 \uc815\ub9ac\uac00 \uc544\ub2c8\ub2e4.\u201d<\/li>\n<\/ol>\n<\/div>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 11.5.<\/span><br \/>\nMU-\uacc4\uc5d0\uc11c \ub2e4\uc74c \ubb38\uc790\uc5f4\uc774 \uc815\ub9ac\uc778\uc9c0 \ud655\uc778\ud558\uc2dc\uc624. \uc815\ub9ac\uc774\uba74 \uc99d\uba85\uc744 \uc81c\uc2dc\ud558\uace0, \uc815\ub9ac\uac00 \uc544\ub2c8\ub77c\uba74 \uc774\uc720\ub97c \uc124\uba85\ud558\uc2dc\uc624.<\/p>\n<ol class=\"parenthesis\">\n<li>MIIII<\/li>\n<li>MUUII<\/li>\n<li>MUIIII<\/li>\n<li>MUIUIU<\/li>\n<li>MIII<\/li>\n<\/ol>\n<\/div>\n<p>\uc774\uc81c \ub2e4\uc74c\uacfc \uac19\uc740 \uc9c8\ubb38\uc744 \uc0dd\uac01\ud574 \ubcf4\uc790.<\/p>\n<p style=\"text-align: center;\">\u201c\\(\\mathrm{MU}\\)\ub294 \uc815\ub9ac\uc778\uac00?\u201d<\/p>\n<p>\uc774 \uc9c8\ubb38\uc5d0 \ub2f5\ud558\uae30 \uc704\ud574 MU-\uacc4\uc5d0 \uad00\ud55c \ub2e4\uc74c \uba54\ud0c0\uc815\ub9ac\ub97c \uc99d\uba85\ud558\uc790.<\/p>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 11.6.<\/span><br \/>\n\ubb38\uc790\uc5f4 \\(w\\)\uc5d0 \ub098\ud0c0\ub098\ub294 \\(\\mathrm{I}\\)\uc758 \uac1c\uc218\ub97c \\(N_{\\mathrm I}(w)\\)\ub77c\uace0 \ud558\uc790. \ud55c \ucd94\ub860 \uaddc\uce59\uc744 \uc801\uc6a9\ud558\uae30 \uc804\uc758 \ubb38\uc790\uc5f4\uc744 \\(s\\), \uc801\uc6a9\ud55c \ub4a4\uc758 \ubb38\uc790\uc5f4\uc744 \\(t\\)\ub77c\uace0 \ud560 \ub54c \ub2e4\uc74c \ubb3c\uc74c\uc5d0 \ub2f5\ud558\uc2dc\uc624.<\/p>\n<ol class=\"parenthesis\">\n<li>\ub124 \ucd94\ub860 \uaddc\uce59 \uac01\uac01\uc5d0 \ub300\ud558\uc5ec \\(N_{\\mathrm I}(t)\\)\ub97c \\(N_{\\mathrm I}(s)\\)\ub85c \ub098\ud0c0\ub0b4\uc2dc\uc624.<\/li>\n<li>\\(N_{\\mathrm I}(s)\\)\ub97c \\(3\\)\uc73c\ub85c \ub098\ub208 \ub098\uba38\uc9c0\uac00 \\(1\\) \ub610\ub294 \\(2\\)\uc774\uba74 \\(N_{\\mathrm I}(t)\\)\ub3c4 \\(3\\)\uc758 \ubc30\uc218\uac00 \ub420 \uc218 \uc5c6\uc74c\uc744 \ud655\uc778\ud558\uc2dc\uc624.<\/li>\n<li>\uacf5\ub9ac \\(\\mathrm{MI}\\)\uc5d0\uc11c \uc2dc\uc791\ud558\ub294 \uc5b4\ub5a4 \uc99d\uba85\uc5d0\uc11c\ub3c4 \ub9c8\uc9c0\ub9c9 \ubb38\uc790\uc5f4\uc758 \\(\\mathrm{I}\\)\uc758 \uac1c\uc218\uac00 \\(3\\)\uc758 \ubc30\uc218\uac00 \ub420 \uc218 \uc5c6\uc744 \uac83\uc774\ub77c\uace0 \uc608\uc0c1\ud560 \uc218 \uc788\ub294 \uc774\uc720\ub97c \uc124\uba85\ud558\uc2dc\uc624.<\/li>\n<\/ol>\n<\/div>\n<div class=\"box theorem\">\n<p><span class=\"definition\">\uc815\ub9ac 11.4.<\/span><\/p>\n<p>MU-\uacc4\uc758 \uc815\ub9ac\uc5d0\uc11c \\(\\mathrm{I}\\)\uac00 \ub098\ud0c0\ub098\ub294 \ud69f\uc218\ub294 \\(3\\)\uc758 \ubc30\uc218\uac00 \uc544\ub2c8\ub2e4.<\/p>\n<\/div>\n<div class=\"proof\">\n<p class=\"proofbegin\"><span class=\"proof\">\uc99d\uba85<\/span><br \/>\n\uc99d\uba85 \uae38\uc774\uc5d0 \ub300\ud55c \uc218\ud559\uc801 \uadc0\ub0a9\ubc95\uc744 \uc0ac\uc6a9\ud55c\ub2e4. \uc99d\uba85 \uae38\uc774\uac00 \\(1\\)\uc774\uba74 \ub9c8\uc9c0\ub9c9 \ub17c\ub9ac\uc2dd\uc740 \uacf5\ub9ac \\(\\mathrm{MI}\\)\uc774\uace0, \\(\\mathrm{I}\\)\uc758 \uac1c\uc218\ub294 \\(1\\)\uc774\ubbc0\ub85c \uc8fc\uc7a5\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<p>\uae38\uc774\uac00 \\(n\\) \uc774\ud558\uc778 \ubaa8\ub4e0 \uc99d\uba85\uc758 \ub9c8\uc9c0\ub9c9 \ub17c\ub9ac\uc2dd\uc5d0\uc11c \uc8fc\uc7a5\uc774 \uc131\ub9bd\ud55c\ub2e4\uace0 \uac00\uc815\ud558\uace0, \uae38\uc774\uac00 \\(n+1\\)\uc778 \uc99d\uba85\uc758 \ub9c8\uc9c0\ub9c9 \ub17c\ub9ac\uc2dd\uc744 \\(t\\)\ub77c\uace0 \ud558\uc790. \\(t\\)\uac00 \uacf5\ub9ac\uac00 \uc544\ub2c8\uba74 MU-\uacc4\uc758 \uac01 \ucd94\ub860 \uaddc\uce59\uc740 \uc804\uc81c\ub97c \ud558\ub098\ub9cc \uac00\uc9c0\ubbc0\ub85c, \\(t\\)\ub294 \uae38\uc774\uac00 \\(n\\) \uc774\ud558\uc778 \uc99d\uba85\uc744 \uac16\ub294 \uc5b4\ub5a4 \uc815\ub9ac \\(s\\)\uc5d0 \ud55c \ucd94\ub860 \uaddc\uce59\uc744 \uc801\uc6a9\ud558\uc5ec \uc5bb\uc5b4\uc9c4\ub2e4. \\(s\\)\uc5d0 \ub098\ud0c0\ub098\ub294 \\(\\mathrm{I}\\)\uc758 \uac1c\uc218\ub97c \\(x\\), \\(t\\)\uc5d0 \ub098\ud0c0\ub098\ub294 \\(\\mathrm{I}\\)\uc758 \uac1c\uc218\ub97c \\(y\\)\ub77c\uace0 \ud558\uc790. \uadc0\ub0a9\uac00\uc815\uc5d0 \uc758\ud574 \\(3\\nmid x\\)\uc774\ub2e4.<\/p>\n<p>\uaddc\uce59 1\uacfc \uaddc\uce59 4\uc5d0\uc11c\ub294 \\(y=x\\)\uc774\ub2e4. \uaddc\uce59 2\uc5d0\uc11c\ub294 \\(y=2x\\)\uc774\ubbc0\ub85c \\(3\\nmid y\\)\uc774\ub2e4. \uaddc\uce59 3\uc5d0\uc11c\ub294 \\(y=x-3\\)\uc774\ubbc0\ub85c \\(y\\equiv x\\pmod 3\\)\uc774\ub2e4. \ub530\ub77c\uc11c \uc5b4\ub290 \uacbd\uc6b0\uc5d0\ub3c4 \\(3\\nmid y\\)\uc774\uace0, \uc218\ud559\uc801 \uadc0\ub0a9\ubc95\uc5d0 \uc758\ud574 \uc815\ub9ac\uac00 \uc99d\uba85\ub41c\ub2e4.<span class=\"qed\"><\/span><\/p>\n<\/div>\n<p>\ubb38\uc790\uc5f4 \\(\\mathrm{MU}\\)\uc5d0\ub294 \\(\\mathrm{I}\\)\uac00 \\(0\\)\uac1c \ub098\ud0c0\ub098\uba70 \\(0\\)\uc740 \\(3\\)\uc758 \ubc30\uc218\uc774\ub2e4. \ub530\ub77c\uc11c \uc815\ub9ac 11.4\uc5d0 \uc758\ud574 \\(\\mathrm{MU}\\)\ub294 MU-\uacc4\uc758 \uc815\ub9ac\uac00 \uc544\ub2c8\ub2e4.<\/p>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 11.7.<\/span><br \/>\nMU-\uacc4\uc758 \ucd94\ub860 \uaddc\uce59\uc744 \uc0ac\uc6a9\ud558\uc5ec \ub2e4\uc74c \ubb3c\uc74c\uc5d0 \ub2f5\ud558\uc2dc\uc624.<\/p>\n<ol class=\"parenthesis\">\n<li>\\(\\mathrm{MIII}\\)\ub85c\ubd80\ud130 \\(\\mathrm{MU}\\)\ub97c \uc720\ub3c4\ud560 \uc218 \uc788\ub294\uac00?<\/li>\n<li>\\(\\mathrm{MIIIIII}\\)\ub85c\ubd80\ud130 \\(\\mathrm{MUI}\\)\ub97c \uc720\ub3c4\ud560 \uc218 \uc788\ub294\uac00?<\/li>\n<li>\\(\\mathrm{MUUIII}\\)\ub85c\ubd80\ud130 \\(\\mathrm{MIII}\\)\ub97c \uc720\ub3c4\ud560 \uc218 \uc788\ub294\uac00?<\/li>\n<\/ol>\n<\/div>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 11.8.<\/span><br \/>\nMU-\uacc4\uc5d0\uc11c \\(\\mathrm{U}\\)\uc758 \uac1c\uc218\uc5d0 \ub300\ud55c \ub2e4\uc74c \uba85\uc81c\ub97c \uc99d\uba85\ud558\uac70\ub098 \ubc18\ub840\ub97c \uc81c\uc2dc\ud558\uc2dc\uc624.<\/p>\n<ol class=\"parenthesis\">\n<li>MU-\uacc4\uc758 \ubaa8\ub4e0 \uc815\ub9ac\ub294 \\(\\mathrm{U}\\)\ub97c \uc9dd\uc218 \uac1c \ud3ec\ud568\ud55c\ub2e4.<\/li>\n<li>\\(\\mathrm{M}\\)\uc73c\ub85c \uc2dc\uc791\ud558\uace0 \\(\\mathrm{U}\\)\ub97c \uc815\ud655\ud788 \\(1\\)\uac1c \ud3ec\ud568\ud558\ub294 \ubaa8\ub4e0 \ubb38\uc790\uc5f4\uc740 \uc815\ub9ac\uc774\ub2e4.<\/li>\n<li>MU-\uacc4\uc758 \uc815\ub9ac\uc5d0\uc11c \\(\\mathrm{U}\\)\uc758 \uac1c\uc218\uc5d0\ub294 \ucd5c\ub313\uac12\uc774 \uc874\uc7ac\ud55c\ub2e4.<\/li>\n<\/ol>\n<\/div>\n<div class=\"problem\">\n<p><span class=\"problem\">\ubb38\uc81c 11.9.<\/span><br \/>\n\uc815\ub9ac 11.4\uc758 \ubd80\ubd84\uc801\uc778 \uc5ed\uc744 \uc99d\uba85\ud558\uc2dc\uc624. \uc989 \\(x\\)\uac00 \\(\\mathrm{I}\\)\uc640 \\(\\mathrm{U}\\)\ub9cc\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \ubb38\uc790\uc5f4\uc774\uace0 \\(x\\)\uc5d0 \ub098\ud0c0\ub098\ub294 \\(\\mathrm{I}\\)\uc758 \uac1c\uc218\uac00 \\(3\\)\uc758 \ubc30\uc218\uac00 \uc544\ub2c8\uba74 \\(\\mathrm{M}x\\)\ub294 MU-\uacc4\uc758 \uc815\ub9ac\uc784\uc744 \uc99d\uba85\ud558\uc2dc\uc624. (\\(x\\)\uc758 \uac01 \\(\\mathrm{U}\\)\ub97c \\(\\mathrm{III}\\)\ub85c \ubc14\uafb8\uc5b4 \uc5bb\ub294 \ubb38\uc790\uc5f4\uc744 \uc0dd\uac01\ud55c\ub2e4. \ub610\ud55c \\(r\\ge4\\)\uc77c \ub54c \uaddc\uce59 1, \uaddc\uce59 3, \uaddc\uce59 4\ub97c \ucc28\ub840\ub85c \uc0ac\uc6a9\ud558\uba74 \\(\\mathrm{MI}^r\\)\uc5d0\uc11c \\(\\mathrm{MI}^{r-3}\\)\uc744 \uc720\ub3c4\ud560 \uc218 \uc788\ub2e4.)<\/p>\n<\/div>\n<div class=\"box theorem\">\n<p><span class=\"definition\">\uc815\ub9ac 11.5. (MU-\uacc4 \uc815\ub9ac\uc758 \uc870\uac74)<\/span><\/p>\n<p>\ube44\uc5b4 \uc788\uc9c0 \uc54a\uc740 \ubb38\uc790\uc5f4 \\(w\\)\uac00 MU-\uacc4\uc758 \uc815\ub9ac\uc77c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740 \uc5b4\ub5a4 \\(\\mathrm{I}\\)\uc640 \\(\\mathrm{U}\\)\ub9cc\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \ubb38\uc790\uc5f4 \\(x\\)\uac00 \uc874\uc7ac\ud558\uc5ec \\(w=\\mathrm{M}x\\)\uc774\uace0, \\(x\\)\uc5d0 \ub098\ud0c0\ub098\ub294 \\(\\mathrm{I}\\)\uc758 \uac1c\uc218\uac00 \\(3\\)\uc758 \ubc30\uc218\uac00 \uc544\ub2cc \uac83\uc774\ub2e4.<\/p>\n<\/div>\n<p>\uc815\ub9ac 11.4\uc640 \ubb38\uc81c 11.9\ub97c \ud569\uce58\uba74 \uc815\ub9ac 11.5\ub97c \uc5bb\ub294\ub2e4. \ub530\ub77c\uc11c MU-\uacc4\uc5d0\uc11c\ub294 \uc8fc\uc5b4\uc9c4 \ubb38\uc790\uc5f4\uc774 \uc815\ub9ac\uc778\uc9c0 \uc5ec\ubd80\ub97c \uc2e4\uc81c\ub85c \uacb0\uc815\ud560 \uc218 \uc788\ub2e4. \uc774\ub294 \ud615\uc2dd\uacc4\uc5d0 \ub530\ub77c \uc815\ub9ac \uc5ec\ubd80\uc758 \uacb0\uc815\uac00\ub2a5\uc131\uc774 \ub2ec\ub77c\uc9c8 \uc218 \uc788\ub2e4\ub294 \uc55e\uc758 \uc124\uba85\uc744 \ubcf4\uc5ec \uc8fc\ub294 \uac04\ub2e8\ud55c \uc608\uc774\ub2e4.<\/p>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 11.10.<\/span><br \/>\n\uc815\ub9ac 11.5\ub97c \uc0ac\uc6a9\ud558\uc5ec \ub2e4\uc74c \ubb38\uc790\uc5f4\uc774 MU-\uacc4\uc758 \uc815\ub9ac\uc778\uc9c0 \ud310\uc815\ud558\uc2dc\uc624. \uc774 \ubb38\uc81c\uc5d0\uc11c\ub294 \uc2e4\uc81c \uc99d\uba85\uc744 \uad6c\uc131\ud558\uc9c0 \uc54a\uc544\ub3c4 \ub41c\ub2e4.<\/p>\n<ol class=\"parenthesis\">\n<li>\\(\\mathrm{MI}\\)<\/li>\n<li>\\(\\mathrm{MU}\\)<\/li>\n<li>\\(\\mathrm{MIIIU}\\)<\/li>\n<li>\\(\\mathrm{MUUII}\\)<\/li>\n<li>\\(\\mathrm{UMI}\\)<\/li>\n<li>\\(\\mathrm{MMII}\\)<\/li>\n<\/ol>\n<\/div>\n<div class=\"contentbottombox\">\n<p class=\"contentbottomboxtitle\"><a href=\"\/blog\/invitation-to-mathematical-logic\/\">\uc9d1\ud569\uacfc \uc218\ub9ac\ub17c\ub9ac \uccab\uac78\uc74c \ubaa9\ucc28 \ubcf4\uae30<\/a><\/p>\n<p><span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch01-naive-logic\/\">\uba85\uc81c\uc640 \ub17c\ub9ac<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch02-sets\">\uc9d1\ud569\uc758 \uac1c\ub150<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch03-algebra-of-classes\">\ub2e4\uc591\ud55c \uc9d1\ud569\uc758 \uc5f0\uc0b0<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch04-relations-and-functions\">\uad00\uacc4\uc640 \ud568\uc218<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch05-infinite-sets\">\uc720\ud55c\uc9d1\ud569\uacfc \ubb34\ud55c\uc9d1\ud569<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch06-natural-numbers\">\uc790\uc5f0\uc218<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch07-cardinal-numbers\">\uc9d1\ud569\uc758 \uae30\uc218<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch08-ordinal-numbers\">\uc9d1\ud569\uc758 \uc11c\uc218<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch09-axiomatic-set-theory\">\uc9d1\ud569\ub860\uc758 \uacf5\ub9ac<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch10-axiom-of-choice\">\uc120\ud0dd \uacf5\ub9ac<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch11-formal-logic\">\ud615\uc2dd\ub17c\ub9ac<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch12-propositional-logic\">\uba85\uc81c\ub17c\ub9ac\uc758 \uac1c\ub150<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch13-soundness-completeness-proplogic\">\uba85\uc81c\ub17c\ub9ac\uc758 \uac74\uc804\uc131\uacfc \uc644\uc804\uc131<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch14-syntax-first-order-logic\">\uc77c\uacc4\ub17c\ub9ac\uc758 \uad6c\ubb38\ub860<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch15-semantics-first-order-logic\">\uc77c\uacc4\ub17c\ub9ac\uc758 \uc758\ubbf8\ub860<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch16-inference-rule-first-order-logic\">\uc77c\uacc4\ub17c\ub9ac\uc758 \ucd94\ub860\uaddc\uce59<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch17-compactness-first-order-logic\">\uc77c\uacc4\ub17c\ub9ac\uc758 \ucf64\ud329\ud2b8\uc131<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch18-peano-arithmetics\">\ud398\uc544\ub178 \uc0b0\uc220<\/a><\/span><br \/>\n<span class=\"contentboxindex\"><a href=\"\/blog\/invitation-to-mathematical-logic\/ch19-incompleteness-theorem\">\ubd88\uc644\uc804\uc131 \uc815\ub9ac<\/a><\/span>\n<\/div>\n<\/div>\n<p><!-- ################## --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>1\uc7a5\uc5d0\uc11c\ub294 \uba85\uc81c\uc640 \ub17c\ub9ac \uc5f0\uc0b0, \ucd94\ub860 \uaddc\uce59\uc744 \uc9c1\uad00\uc801\uc778 \uc218\uc900\uc5d0\uc11c \ub2e4\ub8e8\uc5c8\ub2e4. \uc218\ud559\uc801 \ucd94\ub860\uc744 \uc5c4\ubc00\ud558\uac8c \ubd84\uc11d\ud558\uace0 \uba85\ub8cc\ud55c \uc808\ucc28\uc5d0 \ub530\ub77c \uac80\uc99d\ud558\ub824\uba74 \uc774\ub7ec\ud55c \ub17c\ub9ac\ub97c \ud615\uc2dd\uc801 \uae30\ud638 \uccb4\uacc4\ub85c \ud45c\ud604\ud560 \ud544\uc694\uac00 \uc788\ub2e4. \ud615\uc2dd\ub17c\ub9ac\ub294 \uc77c\uc0c1 \uc5b8\uc5b4\uc758 \ubaa8\ud638\ud568\uc744 \uc904\uc774\uace0 \uba85\ud655\ud55c \uad6c\ubb38 \uaddc\uce59\uacfc \ucd94\ub860 \uaddc\uce59\uc5d0 \ub530\ub77c \ub17c\ub9ac\uc801 \ucd94\ub860\uc744 \uc804\uac1c\ud558\uac8c \ud574 \uc8fc\ub294 \uccb4\uacc4\uc774\ub2e4. \uc218\ud559\uc5d0\uc11c \uc8fc\ub85c \uc0ac\uc6a9\ud558\ub294 \ud615\uc2dd\ub17c\ub9ac\ub294 \ud06c\uac8c \uba85\uc81c\ub17c\ub9ac\uc640 \uc77c\uacc4\ub17c\ub9ac\uac00 \uc788\ub2e4. \uba85\uc81c\ub17c\ub9ac\ub294 \uba85\uc81c\ub4e4 \uc0ac\uc774\uc758 \ub17c\ub9ac\uc801 \uad00\uacc4\ub97c \ub2e4\ub8e8\ub294 \uac00\uc7a5 \uae30\ubcf8\uc801\uc778 \ub17c\ub9ac \uccb4\uacc4\uc774\uba70, \uc77c\uacc4\ub17c\ub9ac\ub294 \uc5ec\uae30\uc5d0 \ud55c\uc815\uae30\ud638\uc640 \uad00\uacc4,&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":9246,"menu_order":111,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"class_list":["post-9268","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9268","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/comments?post=9268"}],"version-history":[{"count":13,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9268\/revisions"}],"predecessor-version":[{"id":10088,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9268\/revisions\/10088"}],"up":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9246"}],"wp:attachment":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/media?parent=9268"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}