{"id":9274,"date":"2025-10-17T20:20:35","date_gmt":"2025-10-17T11:20:35","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?page_id=9274"},"modified":"2025-10-20T18:49:06","modified_gmt":"2025-10-20T09:49:06","slug":"ch13-soundness-completeness-proplogic","status":"publish","type":"page","link":"https:\/\/sasamath.com\/blog\/invitation-to-mathematical-logic\/ch13-soundness-completeness-proplogic\/","title":{"rendered":"\uba85\uc81c\ub17c\ub9ac\uc758 \uac74\uc804\uc131\uacfc \uc644\uc804\uc131"},"content":{"rendered":"<div class=\"mathlogic2025\"><!-- ################## --><\/p>\n<p><!-- \n\n<h2>13. \uba85\uc81c\ub17c\ub9ac\uc758 \uac74\uc804\uc131\uacfc \uc644\uc804\uc131<\/h2>\n\n --><\/p>\n<p>\uba85\uc81c\ub17c\ub9ac\ub97c \ub17c\ud560 \ub54c\ub294 \ub450 \uac00\uc9c0 \uad00\uc810\uc5d0\uc11c \uc811\uadfc\ud560 \uc218 \uc788\ub2e4. \ud558\ub098\ub294 <span class=\"defined\">\uad6c\ubb38\ub860\uc801 \uad00\uc810<\/span>\uc774\uba70 \ub2e4\ub978 \ud558\ub098\ub294 <span class=\"defined\">\uc758\ubbf8\ub860\uc801 \uad00\uc810<\/span>\uc774\ub2e4. \uad6c\ubb38\ub860\uc801 \uad00\uc810\uc5d0\uc11c\ub294 \ubb38\uc790\uc5f4\uc758 \uc758\ubbf8\ub97c \uace0\ub824\ud558\uc9c0 \uc54a\uace0 \uc624\uc9c1 \uae30\ud638 \uc0ac\uc774\uc758 \ud615\uc2dd\uc801 \uad00\uacc4\uc5d0\ub9cc \uad00\uc2ec\uc744 \uac00\uc9c4\ub2e4. \ubc18\uba74 \uc758\ubbf8\ub860\uc801 \uad00\uc810\uc5d0\uc11c\ub294 \ub17c\ub9ac\ubcc0\uc218\uc758 \uc9c4\ub9bf\uac12 \ubc30\uc815\uc5d0 \ub530\ub978 \ub17c\ub9ac\uc2dd\uc758 \uc9c4\ub9bf\uac12\uacfc \ub17c\ub9ac\uc2dd \uc0ac\uc774\uc758 \ub17c\ub9ac\uc801 \uadc0\uacb0\uc5d0 \uad00\uc2ec\uc744 \uac00\uc9c4\ub2e4.<\/p>\n<p>\uc774 \ub450 \uad00\uc810\uc740 \uc0c1\ub2f9\ud788 \ub2e4\ub978 \uac83\ucc98\ub7fc \ubcf4\uc774\uc9c0\ub9cc, \uc2e4\uc81c\ub85c\ub294 \ubc00\uc811\ud558\uac8c \uc5f0\uad00\ub418\uc5b4 \uc788\ub2e4. \uc8fc\uc5b4\uc9c4 \uac00\uc815 \ud558\uc5d0\uc11c \uad6c\ubb38\ub860\uc801 \uad00\uc810\uc5d0\uc11c \ud615\uc2dd\uc801\uc73c\ub85c \uc99d\uba85 \uac00\ub2a5\ud55c \ub17c\ub9ac\uc2dd\uc740 \uac00\uc815\uc758 \ub17c\ub9ac\uc801 \uadc0\uacb0\uc774 \ub418\uba70, \uadf8 \uc5ed\ub3c4 \uc131\ub9bd\ud55c\ub2e4. \uc774\ub7ec\ud55c \ub450 \uad00\uc810\uc758 \uc5f0\uacb0\uc740 \uba85\uc81c\ub17c\ub9ac\uc758 <span class=\"defined\">\uac74\uc804\uc131<\/span>\uacfc <span class=\"defined\">\uc644\uc804\uc131<\/span> \uc815\ub9ac\ub97c \ud1b5\ud574 \ud655\ub9bd\ub41c\ub2e4.<\/p>\n<h3>1. \uac74\uc804\uc131\uacfc \uc644\uc804\uc131\uc758 \uc758\ubbf8<\/h3>\n<p><span class=\"defined\">\uac74\uc804\uc131<\/span>(soundness)\uc740 \ud615\uc2dd\uacc4\uc5d0\uc11c\uc758 \uc815\ub9ac\uac00 \ub17c\ub9ac\uc801 \uadc0\uacb0\uc774 \ub418\ub294 \uc131\uc9c8\uc774\ub2e4. \uc989, \ud615\uc2dd\uc801 \ucd94\ub860\uc744 \ud1b5\ud574 \uc5bb\uc5b4\uc9c4 \uacb0\ub860\uc740 \uc758\ubbf8\ub860\uc801\uc73c\ub85c\ub3c4 \ud0c0\ub2f9\ud558\ub2e4\ub294 \uac83\uc744 \uc758\ubbf8\ud55c\ub2e4. \ubc18\uba74, <span class=\"defined\">\uc644\uc804\uc131<\/span>(completeness)\uc740 \ub17c\ub9ac\uc801 \uadc0\uacb0\uc774 \ub418\ub294 \ub17c\ub9ac\uc2dd\uc740 \ud615\uc2dd\uc801\uc73c\ub85c\ub3c4 \ucd94\ub860 \uac00\ub2a5\ud558\ub2e4\ub294 \uc131\uc9c8\uc774\ub2e4.<\/p>\n<p>\uba85\uc81c\ub17c\ub9ac\ub294 \uac74\uc804\uc131\uacfc \uc644\uc804\uc131\uc744 \ubaa8\ub450 \uac16\ucd94\uace0 \uc788\ub2e4. \uc989, \\(\\varSigma\\)\uac00 \ub17c\ub9ac\uc2dd\uc758 \uc9d1\ud569\uc774\uace0 \\(\\sigma\\)\uac00 \ub17c\ub9ac\uc2dd\uc77c \ub54c \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.<br \/>\n\\[\\varSigma \\models \\sigma \\quad \\Longleftrightarrow \\quad \\varSigma \\vdash \\sigma \\]<br \/>\n\uc5ec\uae30\uc11c \\(\\varSigma \\models \\sigma\\)\ub294 &#8220;\\(\\sigma\\)\ub294 \\(\\varSigma\\)\uc758 \ub17c\ub9ac\uc801 \uadc0\uacb0\uc774\ub2e4&#8221;\ub77c\ub294 \uc758\ubbf8\ub860\uc801 \uc8fc\uc7a5\uc774\uace0, \\(\\varSigma \\vdash \\sigma\\)\ub294 &#8220;\\(\\sigma\\)\ub294 \\(\\varSigma\\)\ub85c\ubd80\ud130 \ud615\uc2dd\uc801\uc73c\ub85c \ucd94\ub860\ub420 \uc218 \uc788\ub2e4&#8221;\ub77c\ub294 \uad6c\ubb38\ub860\uc801 \uc8fc\uc7a5\uc774\ub2e4. \uc774 \ub3d9\uce58\uad00\uacc4\uc5d0\uc11c \uc21c\ubc29\ud5a5(\\(\\Rightarrow\\))\uc774 \uc644\uc804\uc131\uc774\uba70, \uc5ed\ubc29\ud5a5(\\(\\Leftarrow\\))\uc774 \uac74\uc804\uc131\uc774\ub2e4.<\/p>\n<h3>2. \uac74\uc804\uc131 \uc815\ub9ac\uc640 \uc644\uc804\uc131 \uc815\ub9ac<\/h3>\n<p>\uac74\uc804\uc131\uacfc \uc644\uc804\uc131\uc744 \uc99d\uba85\ud558\uae30 \uc704\ud574 \uba3c\uc800 \uba87 \uac00\uc9c0 \uc6a9\uc5b4\ub97c \uc815\uc758\ud558\uc790. \\(\\varSigma\\)\uac00 \ub17c\ub9ac\uc2dd\uc758 \uc9d1\ud569\uc77c \ub54c, \ub9cc\uc57d \ub17c\ub9ac\uc2dd \\(\\psi\\)\uac00 \uc874\uc7ac\ud558\uc5ec \\(\\psi\\)\uc640 \\((\\neg\\psi)\\)\uac00 \ubaa8\ub450 \\(\\varSigma\\)\ub85c\ubd80\ud130 \ucd94\ub860 \uac00\ub2a5\ud558\uba74 \\(\\varSigma\\)\ub294 <span class=\"defined\">\uacb0\ud568\uc774 \uc788\ub2e4<\/span>(inconsistent)\ub77c\uace0 \ud55c\ub2e4. \uadf8\ub807\uc9c0 \uc54a\uc740 \uacbd\uc6b0 \\(\\varSigma\\)\ub294 <span class=\"defined\">\ubb34\ubaa8\uc21c\uc774\ub2e4<\/span>(consistent) \ub610\ub294 <span class=\"defined\">\ubb34\uacb0\ud558\ub2e4<\/span>\ub77c\uace0 \ud55c\ub2e4.<\/p>\n<p>\ub2e4\uc74c\uc740 \uba85\uc81c\ub17c\ub9ac\uc758 \uac74\uc804\uc131\uacfc \uc644\uc804\uc131 \uc815\ub9ac\uc774\ub2e4.<\/p>\n<div class=\"box theorem\">\n<p class=\"marginbottomhalf\"><span class=\"definition\">\uc815\ub9ac 13.1. (\uba85\uc81c\ub17c\ub9ac\uc758 \uac74\uc804\uc131\uacfc \uc644\uc804\uc131)<\/span><\/p>\n<p>\uc784\uc758\uc758 \ub17c\ub9ac\uc2dd \uc9d1\ud569 \\(\\varSigma\\)\uc5d0 \ub300\ud558\uc5ec, \\(\\varSigma\\)\uac00 \ubb34\ubaa8\uc21c\uc77c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740 \uac12\ub9e4\uae40 \\(v\\)\uac00 \uc874\uc7ac\ud558\uc5ec \uc784\uc758\uc758 \\(\\sigma \\in \\varSigma\\)\uc5d0 \ub300\ud558\uc5ec \\(v(\\sigma) = \\mathrm{T}\\)\ub97c \ub9cc\uc871\uc2dc\ud0a4\ub294 \uac83\uc774\ub2e4.<\/p>\n<\/div>\n<p>\uc774 \uc815\ub9ac\ub85c\ubd80\ud130 \ub2e4\uc74c\uacfc \uac19\uc740 \uc911\uc694\ud55c \uacb0\uacfc\ub97c \uc5bb\uc744 \uc218 \uc788\ub2e4.<\/p>\n<ol class=\"parenthesis\">\n<li>\ub17c\ub9ac\uc2dd\uc774 \ud56d\uc9c4\uc77c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740 \uc815\ub9ac\uc778 \uac83\uc774\ub2e4.<\/li>\n<li>\\(\\varSigma\\)\uac00 \ub17c\ub9ac\uc2dd\uc758 \uc9d1\ud569\uc774\uace0 \\(\\sigma\\)\uac00 \ub17c\ub9ac\uc2dd\uc77c \ub54c, \\(\\sigma\\)\uac00 \\(\\varSigma\\)\uc758 \ub17c\ub9ac\uc801 \uadc0\uacb0\uc77c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740 \\(\\sigma\\)\uac00 \\(\\varSigma\\)\ub85c\ubd80\ud130 \ucd94\ub860 \uac00\ub2a5\ud55c \uac83\uc774\ub2e4.<\/li>\n<\/ol>\n<h4>\uac74\uc804\uc131 \uc815\ub9ac\uc758 \uc99d\uba85 \uac1c\uc694<\/h4>\n<p>\uac74\uc804\uc131 \uc815\ub9ac\uc758 \uc99d\uba85\uc740 \ub2e4\uc74c \ub450 \uac00\uc9c0 \uc0ac\uc2e4\uc744 \ubc14\ud0d5\uc73c\ub85c \ud55c\ub2e4.<\/p>\n<ol class=\"parenthesis\">\n<li>\ubaa8\ub4e0 \uacf5\ub9ac\ub294 \ud56d\uc9c4\uc774\ub2e4.<\/li>\n<li>\ucd94\ub860\uaddc\uce59 MP\ub294 \uc9c4\ub9bf\uac12\uc744 \ubcf4\uc874\ud55c\ub2e4. \uc989, \\(v(\\phi) = \\mathrm{T}\\)\uc774\uace0 \\(v((\\phi \\to \\psi)) = \\mathrm{T}\\)\uc774\uba74 \\(v(\\psi) = \\mathrm{T}\\)\uc774\ub2e4.<\/li>\n<\/ol>\n<p>\uc774 \ub450 \uac00\uc9c0 \uc0ac\uc2e4\uc744 \ubc14\ud0d5\uc73c\ub85c, \uc99d\uba85 \uae38\uc774\uc5d0 \ub300\ud55c \uc218\ud559\uc801 \uadc0\ub0a9\ubc95\uc744 \uc801\uc6a9\ud558\uc5ec \ubaa8\ub4e0 \uc815\ub9ac\uac00 \ud56d\uc9c4\uc784\uc744 \uc99d\uba85\ud560 \uc218 \uc788\ub2e4. \uc774\ub85c\uc368 \ud615\uc2dd\uc801\uc73c\ub85c \ucd94\ub860 \uac00\ub2a5\ud55c \ubaa8\ub4e0 \uba85\uc81c\ub294 \uc758\ubbf8\ub860\uc801\uc73c\ub85c\ub3c4 \ud0c0\ub2f9\ud558\ub2e4\ub294 \uac74\uc804\uc131\uc774 \uc99d\uba85\ub41c\ub2e4.<\/p>\n<h4>\uc644\uc804\uc131 \uc815\ub9ac\uc758 \uc99d\uba85 \uac1c\uc694<\/h4>\n<p>\uc644\uc804\uc131 \uc815\ub9ac\uc758 \uc99d\uba85\uc740 \ub2e4\uc74c\uacfc \uac19\uc740 \ub2e8\uacc4\ub85c \uc9c4\ud589\ub41c\ub2e4.<\/p>\n<ol class=\"parenthesis\">\n<li>\uba3c\uc800 \\(\\varSigma\\)\uac00 \ubb34\ubaa8\uc21c\uc77c \ub54c, \uc784\uc758\uc758 \ub17c\ub9ac\uc2dd \\(\\phi\\)\uc5d0 \ub300\ud558\uc5ec \\(\\varSigma \\cup \\{\\phi\\}\\)\uc640 \\(\\varSigma \\cup \\{(\\neg \\phi)\\}\\) \uc911 \ud558\ub098\ub294 \ubb34\ubaa8\uc21c\uc784\uc744 \ubcf4\uc778\ub2e4.<\/li>\n<li>\uc774 \uc0ac\uc2e4\uc744 \ud65c\uc6a9\ud558\uc5ec \\(\\varSigma\\)\ub97c \ubb34\ubaa8\uc21c\uc778 \uadf9\ub300 \uc9d1\ud569 \\(\\varSigma^+\\)\ub85c \ud655\uc7a5\ud55c\ub2e4. \uc774 \uacfc\uc815\uc5d0\uc11c \ubaa8\ub4e0 \ub17c\ub9ac\uc2dd \\(\\phi\\)\uc5d0 \ub300\ud574 \\(\\phi\\)\uc640 \\((\\neg \\phi)\\) \uc911 \uc815\ud655\ud788 \ud558\ub098\ub9cc \\(\\varSigma^+\\)\uc5d0 \uc18d\ud558\ub3c4\ub85d \ud55c\ub2e4.<\/li>\n<li>\uac12\ub9e4\uae40 \ud568\uc218 \\(v\\)\ub97c \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4.<br \/>\n   \\[v(p_i) := \\begin{cases}<br \/>\n   \\mathrm{T} &#038; (p_i \\in \\varSigma^+\\text{\uc77c \ub54c}) \\\\<br \/>\n   \\mathrm{F} &#038; (p_i \\notin \\varSigma^+\\text{\uc77c \ub54c})<br \/>\n   \\end{cases}\\]<\/li>\n<li>\uc218\ud559\uc801 \uadc0\ub0a9\ubc95\uc744 \uc0ac\uc6a9\ud558\uc5ec \uc784\uc758\uc758 \ub17c\ub9ac\uc2dd \\(\\phi\\)\uc5d0 \ub300\ud574 \\(v(\\phi) = \\mathrm{T}\\)\uc77c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc774 \\(\\phi \\in \\varSigma^+\\)\uc784\uc744 \uc99d\uba85\ud55c\ub2e4.<\/li>\n<li>\uc774\ub85c\uc368 \\(\\varSigma\\)\uc5d0 \uc18d\ud558\ub294 \ubaa8\ub4e0 \ub17c\ub9ac\uc2dd\uc774 \ucc38\uc774 \ub418\ub3c4\ub85d \ud558\ub294 \uac12\ub9e4\uae40\uc774 \uc874\uc7ac\ud558\uace0, \ub530\ub77c\uc11c \uc758\ubbf8\ub860\uc801\uc73c\ub85c \ud0c0\ub2f9\ud55c \ubaa8\ub4e0 \uba85\uc81c\ub294 \ud615\uc2dd\uc801\uc73c\ub85c\ub3c4 \ucd94\ub860 \uac00\ub2a5\ud558\ub2e4\ub294 \uc644\uc804\uc131\uc774 \uc99d\uba85\ub41c\ub2e4.<\/li>\n<\/ol>\n<div class=\"problem\">\n<p><span class=\"problem\">\ubb38\uc81c 13.1.<\/span><br \/>\n\ud615\uc2dd\uacc4\uc758 \ubb34\ubaa8\uc21c\uc131\uc5d0 \ub300\ud574 \ub2e4\uc74c\uc744 \ub2f5\ud558\uc2dc\uc624.<\/p>\n<ol class=\"parenthesis\">\n<li>MU-\uacc4\uc5d0\uc11c \ubd80\uc815 \uae30\ud638\uac00 \uc815\uc758\ub418\uc9c0 \uc54a\uc558\ub294\ub370, \uc774 \ud615\uc2dd\uacc4\uc758 \ubb34\ubaa8\uc21c\uc131\uc744 \uc5b4\ub5bb\uac8c \uc815\uc758\ud560 \uc218 \uc788\ub294\uac00?<\/li>\n<li>\ubaa8\ub4e0 \ubb38\uc790\uc5f4\uc774 \uc815\ub9ac\uac00 \ub418\ub294 \ud615\uc2dd\uacc4\ub294 \ubb34\ubaa8\uc21c\uc778\uac00?<\/li>\n<li>\uacf5\ub9ac\uac00 \uc5c6\ub294 \ud615\uc2dd\uacc4\ub294 \ud56d\uc0c1 \ubb34\ubaa8\uc21c\uc778\uac00?<\/li>\n<\/ol>\n<\/div>\n<h3>3. \uba85\uc81c\ub17c\ub9ac\uc758 \ucf64\ud329\ud2b8\uc131<\/h3>\n<p>\uba85\uc81c\ub17c\ub9ac\uc758 \uac74\uc804\uc131\uacfc \uc644\uc804\uc131\uc73c\ub85c\ubd80\ud130 \uc911\uc694\ud55c \uacb0\uacfc\uc778 <span class=\"defined\">\ucf64\ud329\ud2b8\uc131<\/span>\uc774 \ub3c4\ucd9c\ub41c\ub2e4. \ucf64\ud329\ud2b8\uc131\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ub41c\ub2e4.<\/p>\n<div class=\"box theorem\">\n<p><span class=\"definition\">\uc815\ub9ac 13.2. (\uba85\uc81c\ub17c\ub9ac\uc758 \ucf64\ud329\ud2b8\uc131)<\/span><\/p>\n<p>\\(\\varSigma\\)\uac00 \ub17c\ub9ac\uc2dd\uc758 \uc9d1\ud569\uc77c \ub54c, \ub9cc\uc57d \\(\\varSigma\\)\uc758 \uc784\uc758\uc758 \uc720\ud55c\ubd80\ubd84\uc9d1\ud569\uc774 \ub9cc\uc871\ub420 \uc218 \uc788\ub2e4\uba74(satisfiable) \\(\\varSigma\\) \uc790\uccb4\ub3c4 \ub9cc\uc871\ub420 \uc218 \uc788\ub2e4.<\/p>\n<\/div>\n<p>\uc5ec\uae30\uc11c \uc9d1\ud569\uc774 &#8216;\ub9cc\uc871\ub420 \uc218 \uc788\ub2e4'(satisfiable)\ub294 \uac83\uc740 \uac12\ub9e4\uae40 \ud568\uc218 \\(v\\)\uac00 \uc874\uc7ac\ud558\uc5ec \ud574\ub2f9 \uc9d1\ud569\uc758 \ubaa8\ub4e0 \ub17c\ub9ac\uc2dd\uc5d0 \ub300\ud574 \\(v(\\sigma) = \\mathrm{T}\\)\ub97c \ub9cc\uc871\uc2dc\ud0a8\ub2e4\ub294 \uc758\ubbf8\uc774\ub2e4.<\/p>\n<p>\ucf64\ud329\ud2b8\uc131 \uc815\ub9ac\ub294 \uac74\uc804\uc131\uacfc \uc644\uc804\uc131\uc744 \ud65c\uc6a9\ud558\uc5ec \uc99d\uba85\ud560 \uc218 \uc788\ub2e4. \uadf8 \ud575\uc2ec\uc740 \ubaa8\uc21c\uc774 \ub3c4\ucd9c\ub418\ub824\uba74 \ubc18\ub4dc\uc2dc \uc720\ud55c \uac1c\uc758 \ub17c\ub9ac\uc2dd\ub9cc\uc774 \ud544\uc694\ud558\ub2e4\ub294 \uc0ac\uc2e4\uc5d0 \uc788\ub2e4. \ub530\ub77c\uc11c \ubaa8\ub4e0 \uc720\ud55c\ubd80\ubd84\uc9d1\ud569\uc774 \ub9cc\uc871\ub420 \uc218 \uc788\ub2e4\uba74, \ubaa8\uc21c\uc774 \ub3c4\ucd9c\ub420 \uc218 \uc5c6\uace0 \uc804\uccb4 \uc9d1\ud569 \uc5ed\uc2dc \ub9cc\uc871\ub420 \uc218 \uc788\ub2e4.<\/p>\n<h3>4. \ucf64\ud329\ud2b8\uc131\uc758 \uc751\uc6a9: \ud3c9\uba74\uc9c0\ub3c4\uc758 \uc0ac\uc0c9 \uc815\ub9ac<\/h3>\n<p>\uba85\uc81c\ub17c\ub9ac\uc758 \ucf64\ud329\ud2b8\uc131\uc740 \uc218\ud559\uc758 \uc5ec\ub7ec \ubd84\uc57c\uc5d0 \ud65c\uc6a9\ub41c\ub2e4. \ud2b9\ud788 \uc8fc\ubaa9\ud560 \ub9cc\ud55c \uc751\uc6a9 \uc911 \ud558\ub098\ub294 \uc720\ud55c\ud3c9\uba74\uc9c0\ub3c4\uc758 \uc0ac\uc0c9 \uc815\ub9ac\ub97c \ubb34\ud55c\ud3c9\uba74\uc9c0\ub3c4\ub85c \ud655\uc7a5\ud558\ub294 \uac83\uc774\ub2e4.<\/p>\n<div class=\"box theorem\">\n<p><span class=\"definition\">\uc815\ub9ac 13.3. (\uc720\ud55c\ud3c9\uba74\uc9c0\ub3c4\uc758 \uc0ac\uc0c9 \uc815\ub9ac)<\/span><\/p>\n<p>\uc784\uc758\uc758 \uc720\ud55c\ud3c9\uba74\uc9c0\ub3c4\ub97c \ucc44\uc0c9\ud558\ub294 \ub370\uc5d0\ub294 4\uac00\uc9c0 \uc0c9\uc774\uba74 \ucda9\ubd84\ud558\ub2e4.<\/p>\n<\/div>\n<p>\uc774 \uc815\ub9ac\ub294 1976\ub144 \uc544\ud3a0(Kenneth Appel)\uacfc \ud558\ucf04(Wolfgang Haken)\uc774 \ucef4\ud4e8\ud130\uc758 \ub3c4\uc6c0\uc744 \ubc1b\uc544 \uc99d\uba85\ud55c \uac83\uc73c\ub85c \uc720\uba85\ud558\ub2e4. \uba85\uc81c\ub17c\ub9ac\uc758 \ucf64\ud329\ud2b8\uc131\uc744 \ud65c\uc6a9\ud558\uba74 \uc774 \uc815\ub9ac\ub97c \ubb34\ud55c\ud3c9\uba74\uc9c0\ub3c4\ub85c \ud655\uc7a5\ud560 \uc218 \uc788\ub2e4.<\/p>\n<div class=\"box theorem\">\n<p><span class=\"definition\">\uc815\ub9ac 13.4. (\ud3c9\uba74\uc9c0\ub3c4\uc758 \uc0ac\uc0c9 \uc815\ub9ac)<\/span><\/p>\n<p>\uc784\uc758\uc758 \ud3c9\uba74\uc9c0\ub3c4(\uc720\ud55c \ub610\ub294 \ubb34\ud55c)\ub97c \ucc44\uc0c9\ud558\ub294 \ub370\uc5d0\ub294 4\uac00\uc9c0 \uc0c9\uc774\uba74 \ucda9\ubd84\ud558\ub2e4.<\/p>\n<\/div>\n<p>\uc774 \ud655\uc7a5\uc758 \ud575\uc2ec \uc544\uc774\ub514\uc5b4\ub294 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\n<ol class=\"parenthesis\">\n<li>\ubb34\ud55c\ud3c9\uba74\uc9c0\ub3c4\uc758 \uac01 \uad6d\uac00\uc5d0 \ub300\uc751\ud558\ub294 \uba85\uc81c\ubcc0\uc218\ub97c \ub3c4\uc785\ud55c\ub2e4.<\/li>\n<li>\uac01 \uad6d\uac00\uac00 \uc815\ud655\ud788 \ud558\ub098\uc758 \uc0c9\uc744 \uac00\uc9c0\ub3c4\ub85d \ud558\ub294 \ub17c\ub9ac\uc2dd\uacfc, \uc778\uc811\ud55c \uad6d\uac00\uac00 \uc11c\ub85c \ub2e4\ub978 \uc0c9\uc744 \uac00\uc9c0\ub3c4\ub85d \ud558\ub294 \ub17c\ub9ac\uc2dd\uc744 \uc815\uc758\ud55c\ub2e4.<\/li>\n<li>\uc774 \ub17c\ub9ac\uc2dd\ub4e4\uc758 \uc9d1\ud569\uc758 \uc784\uc758\uc758 \uc720\ud55c\ubd80\ubd84\uc9d1\ud569\uc740 \uc720\ud55c\ud3c9\uba74\uc9c0\ub3c4\uc5d0 \ub300\uc751\ub418\ubbc0\ub85c, \uc720\ud55c\ud3c9\uba74\uc9c0\ub3c4\uc758 \uc0ac\uc0c9 \uc815\ub9ac\uc5d0 \uc758\ud574 \ub9cc\uc871\ub420 \uc218 \uc788\ub2e4.<\/li>\n<li>\ucf64\ud329\ud2b8\uc131 \uc815\ub9ac\uc5d0 \uc758\ud574 \uc804\uccb4 \ub17c\ub9ac\uc2dd \uc9d1\ud569\ub3c4 \ub9cc\uc871\ub420 \uc218 \uc788\uc73c\ubbc0\ub85c, \ubb34\ud55c\ud3c9\uba74\uc9c0\ub3c4 \uc5ed\uc2dc 4\uc0c9\uc73c\ub85c \ucc44\uc0c9 \uac00\ub2a5\ud558\ub2e4.<\/li>\n<\/ol>\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>\uba85\uc81c\ub17c\ub9ac\ub97c \ub17c\ud560 \ub54c\ub294 \ub450 \uac00\uc9c0 \uad00\uc810\uc5d0\uc11c \uc811\uadfc\ud560 \uc218 \uc788\ub2e4. \ud558\ub098\ub294 \uad6c\ubb38\ub860\uc801 \uad00\uc810\uc774\uba70 \ub2e4\ub978 \ud558\ub098\ub294 \uc758\ubbf8\ub860\uc801 \uad00\uc810\uc774\ub2e4. \uad6c\ubb38\ub860\uc801 \uad00\uc810\uc5d0\uc11c\ub294 \ubb38\uc790\uc5f4\uc758 \uc758\ubbf8\ub97c \uace0\ub824\ud558\uc9c0 \uc54a\uace0 \uc624\uc9c1 \uae30\ud638 \uc0ac\uc774\uc758 \ud615\uc2dd\uc801 \uad00\uacc4\uc5d0\ub9cc \uad00\uc2ec\uc744 \uac00\uc9c4\ub2e4. \ubc18\uba74 \uc758\ubbf8\ub860\uc801 \uad00\uc810\uc5d0\uc11c\ub294 \ub17c\ub9ac\ubcc0\uc218\uc758 \uc9c4\ub9bf\uac12 \ubc30\uc815\uc5d0 \ub530\ub978 \ub17c\ub9ac\uc2dd\uc758 \uc9c4\ub9bf\uac12\uacfc \ub17c\ub9ac\uc2dd \uc0ac\uc774\uc758 \ub17c\ub9ac\uc801 \uadc0\uacb0\uc5d0 \uad00\uc2ec\uc744 \uac00\uc9c4\ub2e4. \uc774 \ub450 \uad00\uc810\uc740 \uc0c1\ub2f9\ud788 \ub2e4\ub978 \uac83\ucc98\ub7fc \ubcf4\uc774\uc9c0\ub9cc, \uc2e4\uc81c\ub85c\ub294 \ubc00\uc811\ud558\uac8c \uc5f0\uad00\ub418\uc5b4 \uc788\ub2e4. \uc8fc\uc5b4\uc9c4 \uac00\uc815 \ud558\uc5d0\uc11c \uad6c\ubb38\ub860\uc801 \uad00\uc810\uc5d0\uc11c \ud615\uc2dd\uc801\uc73c\ub85c \uc99d\uba85 \uac00\ub2a5\ud55c \ub17c\ub9ac\uc2dd\uc740&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":9246,"menu_order":113,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"class_list":["post-9274","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9274","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=9274"}],"version-history":[{"count":4,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9274\/revisions"}],"predecessor-version":[{"id":9408,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9274\/revisions\/9408"}],"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=9274"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}