{"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":"2025-10-20T18:49:00","modified_gmt":"2025-10-20T09:49:00","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>\uc218\ud559\uc801 \ucd94\ub860\uc744 \uc5c4\ubc00\ud558\uac8c \ubd84\uc11d\ud558\uace0 \uae30\uacc4\uc801\uc73c\ub85c \uac80\uc99d\ud558\uae30 \uc704\ud574\uc11c\ub294 \ub17c\ub9ac\ub97c \ud615\uc2dd\uc801 \uae30\ud638 \uccb4\uacc4\ub85c \ud45c\ud604\ud574\uc57c \ud55c\ub2e4. \ud615\uc2dd\ub17c\ub9ac\ub294 \uc77c\uc0c1 \uc5b8\uc5b4\uc758 \ubaa8\ud638\ud568\uc744 \ubc30\uc81c\ud558\uace0 \uba85\ud655\ud55c \uaddc\uce59\uc5d0 \ub530\ub77c \ub17c\ub9ac\uc801 \ucd94\ub860\uc744 \uc804\uac1c\ud560 \uc218 \uc788\uac8c \ud574\uc8fc\ub294 \uac15\ub825\ud55c \ub3c4\uad6c\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\ub85c \ub098\ub25c\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\uc0ac\uc640 \uad00\uacc4, \ud568\uc218 \ub4f1\uc744 \ucd94\uac00\ud558\uc5ec \uc218\ud559\uc758 \ub300\ubd80\ubd84 \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 \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 \ub17c\ub9ac\uc801 \ud0c0\ub2f9\uc131\uc774 \uc815\ud655\ud788 \uc77c\uce58\ud568\uc744 \ud655\uc778\ud558\uace0, \uc774\uac83\uc774 \uc218\ud559\uc758 \uae30\ucd08\uc5d0 \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 class=\"margintop2\">\ud615\uc2dd\ub17c\ub9ac\uc758 \uac1c\ub150<\/h3>\n<p>\ud615\uc2dd\ub17c\ub9ac\ub294 \uc218\ud559\uc801 \ucd94\ub860\uc744 \uc5c4\ubc00\ud558\uac8c \uc815\uc758\ud558\uace0 \uae30\ud638\ub97c \ud1b5\ud574 \ud45c\ud604\ud558\ub294 \uccb4\uacc4\uc774\ub2e4. \uc77c\uc0c1 \uc5b8\uc5b4\uc758 \ubaa8\ud638\ud568\uc744 \ubc30\uc81c\ud558\uace0 \uba85\ud655\ud55c \uaddc\uce59\uc5d0 \ub530\ub77c \ub17c\ub9ac\uc801 \uc0ac\uace0\ub97c \uc804\uac1c\ud560 \uc218 \uc788\ub3c4\ub85d \ud55c\ub2e4. \ud615\uc2dd\ub17c\ub9ac\ub294 \uc218\ud559\uc758 \uae30\ucd08\ub97c \ud655\ub9bd\ud558\ub294 \ub370 \uc911\uc694\ud55c \uc5ed\ud560\uc744 \ud55c\ub2e4.<\/p>\n<p><span class=\"defined\">\ud615\uc2dd\uacc4<\/span>(formal system)\ub294 \ub2e4\uc74c \ub124 \uac00\uc9c0\ub85c \uad6c\uc131\ub41c \uccb4\uacc4\uc774\ub2e4.<\/p>\n<ul>\n<li><span class=\"defined\">\uc54c\ud30c\ubcb3<\/span> \\(A\\): \uae30\ud638\uc758 \uc9d1\ud569\uc774\ub2e4.<\/li>\n<li><span class=\"defined\">\ub17c\ub9ac\uc2dd<\/span>(formula)\uc758 \uc9d1\ud569: \uac01 \ub17c\ub9ac\uc2dd\uc740 \\(A\\)\uc5d0 \uc18d\ud55c \uae30\ud638\ub85c \uc774\ub8e8\uc5b4\uc9c4 \ubb38\uc790\uc5f4\uc774\ub2e4. \uc8fc\uc5b4\uc9c4 \ubb38\uc790\uc5f4\uc774 \ub17c\ub9ac\uc2dd\uc778\uc9c0 \uc5ec\ubd80\ub97c \ud310\ubcc4\ud558\ub294 \ud615\uc2dd\uc801 \uc808\ucc28[\uc758\ubbf8\ub97c \ub530\uc9c0\uc9c0 \uc54a\uace0 \uaddc\uce59\ub9cc\uc744 \uc720\ud55c \ubc88 \uc801\uc6a9\ud558\ub294 \uc808\ucc28]\uac00 \uc874\uc7ac\ud55c\ub2e4.<\/li>\n<li><span class=\"defined\">\uacf5\ub9ac<\/span>(axiom)\uc758 \uc9d1\ud569: \uac01 \uacf5\ub9ac\ub294 \ub17c\ub9ac\uc2dd\uc774\ub2e4. \ubaa8\ub4e0 \ub17c\ub9ac\uc2dd\uc774 \uacf5\ub9ac\uc778 \uac83\uc740 \uc544\ub2c8\uba70, \uc8fc\uc5b4\uc9c4 \ub17c\ub9ac\uc2dd\uc774 \uacf5\ub9ac\uc778\uc9c0 \uc5ec\ubd80\ub97c \ud310\ubcc4\ud558\ub294 \ud615\uc2dd\uc801 \uc808\ucc28\uac00 \uc874\uc7ac\ud55c\ub2e4.<\/li>\n<li><span class=\"defined\">\ucd94\ub860\uaddc\uce59<\/span>(rule of inference): \uac01 \ucd94\ub860\uaddc\uce59\uc740 \uc720\ud55c \uac1c\uc758 \ub17c\ub9ac\uc2dd\uc744 \uc785\ub825\ubc1b\uc544 \ud558\ub098\uc758 \ub17c\ub9ac\uc2dd\uc744 \ucd9c\ub825\ud55c\ub2e4. \ucd94\ub860\uaddc\uce59\uc744 \uc801\uc6a9\ud558\ub294 \ud615\uc2dd\uc801\uc778 \uc808\ucc28\uac00 \uc874\uc7ac\ud55c\ub2e4.<\/li>\n<\/ul>\n<p>\ud615\uc2dd\uacc4\uc5d0\uc11c <span class=\"defined\">\uc99d\uba85<\/span>(proof)\uc774\ub780 \ub17c\ub9ac\uc2dd\uc758 \uc5f4\ub85c, \uac01 \ub17c\ub9ac\uc2dd\uc740 \uacf5\ub9ac\uc774\uac70\ub098 \uc774\uc804 \ud56d\uc5d0 \ub4f1\uc7a5\ud55c \ub17c\ub9ac\uc2dd\uc5d0 \ucd94\ub860\uaddc\uce59\uc744 \uc801\uc6a9\ud558\uc5ec \uc5bb\uc5b4\uc9c4 \uac83\uc774\ub2e4. \uc99d\uba85\uc758 \ub9c8\uc9c0\ub9c9 \ud56d\uc744 <span class=\"defined\">\uc815\ub9ac<\/span>(theorem)\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n<p>\ud558\ub098\uc758 \ud615\uc2dd\uacc4\uc5d0\uc11c \ubaa8\ub4e0 \uc815\ub9ac\ub294 \ud615\uc2dd\uc801\uc778 \uc808\ucc28\uc5d0 \uc758\ud558\uc5ec \uc5bb\uc5b4\uc9c8 \uc218 \uc788\ub2e4. \uadf8\ub7ec\ub098 \uc77c\ubc18\uc801\uc73c\ub85c \uc8fc\uc5b4\uc9c4 \ub17c\ub9ac\uc2dd\uc774 \uc815\ub9ac\uc778\uc9c0 \uc544\ub2cc\uc9c0\ub97c \ud310\ubcc4\ud558\ub294 \uc808\ucc28\ub294 \uc874\uc7ac\ud558\uc9c0 \uc54a\ub294\ub2e4. \ud615\uc2dd\uacc4\uac00 \uac00\uc9c4 \ud2b9\uc131\uc5d0 \ub530\ub77c \uc8fc\uc5b4\uc9c4 \ub17c\ub9ac\uc2dd\uc774 \uc815\ub9ac\uc778\uc9c0\ub97c \ubc1d\ud600\ub0b4\ub294 \uac83\uc774 \uac00\ub2a5\ud560 \uc218\ub3c4 \uc788\uace0 \uadf8\ub807\uc9c0 \uc54a\uc744 \uc218\ub3c4 \uc788\ub2e4.<\/p>\n<p>\ud615\uc2dd\uacc4 \uc790\uccb4\ub97c \uc218\ud559\uc801 \ub300\uc0c1\uc73c\ub85c \ub2e4\ub8e8\uba74 <span class=\"defined\">\uc0c1\uc704\uc218\ud559\uc815\ub9ac<\/span>(metatheorem)[&#8216;\ucd08\uc218\ud559\uc815\ub9ac&#8217; \ub610\ub294 &#8216;\uc218\ud559\uc678\uc801\uc815\ub9ac&#8217;\ub77c\uace0\ub3c4 \ubd80\ub978\ub2e4.]\ub97c \uc5bb\uc744 \uc218 \uc788\ub2e4. \uc774\uac83\uc740 \ud615\uc2dd\uacc4 \uc790\uccb4\uc758 \ud2b9\uc131\uc5d0 \ub300\ud55c \uc815\ub9ac\ub85c\uc11c, \ud615\uc2dd\uacc4 \ub0b4\uc5d0\uc11c \uc5bb\uc5b4\uc9c0\ub294 \uc815\ub9ac\uc640\ub294 \ub2e4\ub978 \uac1c\ub150\uc774\ub2e4.<\/p>\n<h3 class=\"margintop2\">\ud615\uc2dd\uacc4\uc758 \uc608: MU-\uacc4<\/h3>\n<p>\ud615\uc2dd\uacc4\uc758 \uc608\ub85c \ud638\ud504\uc2a4\ud0dc\ud130\uc758 <span class=\"defined\">\\(\\mathrm{MU}\\)-\uacc4<\/span>(MU-system)\ub97c \uc0b4\ud3b4\ubcf4\uc790.<\/p>\n<p>MU-\uacc4\uc5d0\uc11c <span class=\"defined\">\uc54c\ud30c\ubcb3<\/span>\uc740 \uc9d1\ud569 \\(\\left\\{ \\mathrm{M},\\, \\mathrm{I},\\, \\mathrm{U}\\right\\}\\)\uc774\uba70 <span class=\"defined\">\ub17c\ub9ac\uc2dd<\/span>\uc740 \ube44\uc5b4\uc788\uc9c0 \uc54a\uc740 \ubb38\uc790\uc5f4\uc774\ub2e4. \uacf5\ub9ac\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \ub2e8 \ud558\ub098 \uc874\uc7ac\ud55c\ub2e4.<br \/>\n\\[\\mathrm{M I}\\]<br \/>\n\ucd94\ub860\uaddc\uce59\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \ub124 \uac1c\uac00 \uc874\uc7ac\ud55c\ub2e4.<\/p>\n<ul>\n<li>\uaddc\uce59 1. \\(\\mathrm{I}\\)\ub85c \ub05d\ub098\ub294 \ubb38\uc790\uc5f4\uc5d0\ub294 \ub05d\uc5d0 \\(\\mathrm{U}\\)\ub97c \ucd94\uac00\ud560 \uc218 \uc788\ub2e4.<\/li>\n<li>\uaddc\uce59 2. \\(\\mathrm{M}\\)\uc73c\ub85c \uc2dc\uc791\ud558\ub294 \ubb38\uc790\uc5f4 \\(\\mathrm{Mx}\\)\uc5d0 \ub300\ud558\uc5ec \\(\\mathrm{M}\\) \ub4a4\uc5d0 \uc774\uc5b4\uc9c0\ub294 \ubb38\uc790\uc5f4\uc744 \ubcf5\uc81c\ud558\uc5ec \\(\\mathrm{Mxx}\\)\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 \uac1c\uc758 \ubb38\uc790\ub97c \\(\\mathrm{U}\\)\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 \uac1c\uc758 \ubb38\uc790\ub97c \uc5c6\uc568 \uc218 \uc788\ub2e4.<\/li>\n<\/ul>\n<p>MU-\uacc4\uc5d0\uc11c\uc758 \uc99d\uba85\uc758 \uc608\ub85c\uc11c \ub2e4\uc74c\uacfc \uac19\uc740 \uac83\uc744 \ub4e4 \uc218 \uc788\ub2e4.<br \/>\n\\[\\mathrm{MI,} \\quad \\mathrm{MII,} \\quad \\mathrm{MIIII,} \\quad \\mathrm{MUI,} \\quad \\mathrm{MUIU}.\\]<br \/>\n\uc774 \uc99d\uba85\uc740 \uacf5\ub9ac \\(\\mathrm{MI}\\)\ub85c\ubd80\ud130 \uc2dc\uc791\ud558\uc5ec \uaddc\uce59 2\ub97c \ub450 \ubc88 \uc801\uc6a9\ud558\uace0 \uaddc\uce59 3\uacfc \uaddc\uce59 1\uc744 \uc774\uc5b4\uc11c \uc801\uc6a9\ud55c \uac83\uc774\ub2e4.<\/p>\n<div class=\"problem\">\n<p class=\"marginbottomhalf\"><span class=\"problem\">\ubb38\uc81c 11.1.<\/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;\">&#8220;\\(\\mathrm{MU}\\)\ub294 \uc815\ub9ac\uc778\uac00?&#8221;<\/p>\n<p>\uc774 \uc9c8\ubb38\uc5d0 \ub2f5\ud558\uae30 \uc704\ud574 \ub2e4\uc74c\uacfc \uac19\uc740 \uc0c1\uc704\uc218\ud559\uc815\ub9ac\ub97c \ub3c4\uc785\ud558\uc790.<\/p>\n<div class=\"box theorem\">\n<p class=\"marginbottomhalf\"><span class=\"definition\">\uc815\ub9ac 11.1.<\/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=\"proofname\">\uc99d\uba85<\/p>\n<p>\uc99d\uba85 \uae38\uc774\uc5d0 \ub300\ud55c \uc218\ud559\uc801 \uadc0\ub0a9\ubc95\uc744 \uc0ac\uc6a9\ud55c\ub2e4.<\/p>\n<p>\uae30\ubcf8 \ub2e8\uacc4: \uac00\uc7a5 \uc9e7\uc740 \uc99d\uba85\uc740 \uacf5\ub9ac \\(\\mathrm{MI}\\)\ub85c\ub9cc \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \\(\\mathrm{MI}\\)\uc5d0\ub294 \\(\\mathrm{I}\\)\uac00 1\uac1c \ud3ec\ud568\ub418\uc5b4 \uc788\uace0, 1\uc740 3\uc758 \ubc30\uc218\uac00 \uc544\ub2c8\ubbc0\ub85c \uc8fc\uc7a5\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<p>\uadc0\ub0a9 \ub2e8\uacc4: \uc99d\uba85 \uae38\uc774\uac00 \\(n\\)\uc778 \uc815\ub9ac \\(t\\)\uc5d0 \ub300\ud574, \\(t\\)\ub294 \uc99d\uba85 \uae38\uc774\uac00 \\(n-1\\)\uc778 \uc815\ub9ac \\(s\\)\uc5d0 \ucd94\ub860 \uaddc\uce59\uc744 \uc801\uc6a9\ud558\uc5ec \uc5bb\uc5b4\uc9c4 \uac83\uc774\ub2e4. \\(s\\)\uc5d0 \ub098\ud0c0\ub098\ub294 \\(\\mathrm{I}\\)\uc758 \uac1c\uc218\ub97c \\(x\\)\ub77c\uace0 \ud558\uc790. \uadc0\ub0a9\uc801 \uac00\uc815\uc5d0 \uc758\ud558\uc5ec \\(x\\)\ub294 \\(3\\)\uc758 \ubc30\uc218\uac00 \uc544\ub2c8\ub2e4. \\(t\\)\uc5d0 \ub098\ud0c0\ub098\ub294 \\(\\mathrm{I}\\)\uc758 \uac1c\uc218\ub97c \\(y\\)\ub77c\uace0 \ud558\uc790. \uac01 \ucd94\ub860 \uaddc\uce59\uc744 \uc801\uc6a9\ud588\uc744 \ub54c \\(x\\)\uc640 \\(y\\)\uc758 \uad00\uacc4\ub97c \ub4f1\uc2dd\uc73c\ub85c \ub098\ud0c0\ub0b4\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\n<ul style=\"margin-left: 3em;\">\n<li>\uaddc\uce59 1: \\(y=x\\)<\/li>\n<li>\uaddc\uce59 2: \\(y=2x\\)<\/li>\n<li>\uaddc\uce59 3: \\(y=x-3\\)<\/li>\n<li>\uaddc\uce59 4: \\(y=x\\)<\/li>\n<\/ul>\n<p>\uac01 \uacbd\uc6b0\uc5d0 \\(y\\)\ub294 \\(3\\)\uc758 \ubc30\uc218\uac00 \uc544\ub2c8\ub2e4. \ub530\ub77c\uc11c \uc218\ud559\uc801 \uadc0\ub0a9\ubc95\uc5d0 \uc758\ud558\uc5ec \uc815\ub9ac\uac00 \uc99d\uba85\ub418\uc5c8\ub2e4.<span class=\"qed\"><\/span><\/p>\n<\/div>\n<p>\uc704 \uc815\ub9ac\uc5d0 \uc758\ud558\uba74, &#8216;\\(\\mathrm{MU}\\)&#8217;\uc5d0\ub294 \\(\\mathrm{I}\\)\uac00 \uc5c6\uc73c\ubbc0\ub85c \\(\\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 11.2.<\/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 11.3.<\/span><br \/>\nMU-\uacc4\uc5d0\uc11c \\(\\mathrm{U}\\)\uc758 \uac1c\uc218\uc5d0 \ub300\ud55c \ub2e4\uc74c \uba85\uc81c\ub97c \uc99d\uba85 \ub610\ub294 \ubc18\uc99d\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 \ucd5c\ub300 \uac1c\uc218\ub294 \uc874\uc7ac\ud558\ub294\uac00?<\/li>\n<\/ol>\n<\/div>\n<div class=\"problem\">\n<p><span class=\"problem\">\ubb38\uc81c 11.4.<\/span><br \/>\n\uc815\ub9ac 11.1\uc758 (\ubd80\ubd84\uc801\uc778) \uc5ed\uc774 \uc131\ub9bd\ud568\uc744 \uc99d\uba85\ud558\uc2dc\uc624. \uc989 \\(\\mathrm{MU}\\)-\uacc4\uc5d0\uc11c \\(\\mathrm{M}\\)\uc73c\ub85c \uc2dc\uc791\ud558\uace0 \\(\\mathrm{I}\\)\uac00 \ub098\ud0c0\ub098\ub294 \ud69f\uc218\uac00 3\uc758 \ubc30\uc218\uac00 \uc544\ub2cc \ub17c\ub9ac\uc2dd\uc740 \uc815\ub9ac\uc784\uc744 \uc99d\uba85\ud558\uc2dc\uc624.<\/p>\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>\uc218\ud559\uc801 \ucd94\ub860\uc744 \uc5c4\ubc00\ud558\uac8c \ubd84\uc11d\ud558\uace0 \uae30\uacc4\uc801\uc73c\ub85c \uac80\uc99d\ud558\uae30 \uc704\ud574\uc11c\ub294 \ub17c\ub9ac\ub97c \ud615\uc2dd\uc801 \uae30\ud638 \uccb4\uacc4\ub85c \ud45c\ud604\ud574\uc57c \ud55c\ub2e4. \ud615\uc2dd\ub17c\ub9ac\ub294 \uc77c\uc0c1 \uc5b8\uc5b4\uc758 \ubaa8\ud638\ud568\uc744 \ubc30\uc81c\ud558\uace0 \uba85\ud655\ud55c \uaddc\uce59\uc5d0 \ub530\ub77c \ub17c\ub9ac\uc801 \ucd94\ub860\uc744 \uc804\uac1c\ud560 \uc218 \uc788\uac8c \ud574\uc8fc\ub294 \uac15\ub825\ud55c \ub3c4\uad6c\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\ub85c \ub098\ub25c\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\uc0ac\uc640 \uad00\uacc4, \ud568\uc218 \ub4f1\uc744 \ucd94\uac00\ud558\uc5ec \uc218\ud559\uc758 \ub300\ubd80\ubd84 \ub0b4\uc6a9\uc744 \ud45c\ud604\ud560 \uc218 \uc788\uac8c \ud655\uc7a5\ud55c \uccb4\uacc4\uc774\ub2e4. \uc774\ub4e4 \ub17c\ub9ac&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":11,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9268\/revisions"}],"predecessor-version":[{"id":9443,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9268\/revisions\/9443"}],"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}]}}