{"id":9291,"date":"2025-10-17T20:25:39","date_gmt":"2025-10-17T11:25:39","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?page_id=9291"},"modified":"2025-10-20T18:49:29","modified_gmt":"2025-10-20T09:49:29","slug":"ch18-peano-arithmetics","status":"publish","type":"page","link":"https:\/\/sasamath.com\/blog\/invitation-to-mathematical-logic\/ch18-peano-arithmetics\/","title":{"rendered":"\ud398\uc544\ub178 \uc0b0\uc220"},"content":{"rendered":"<div class=\"mathlogic2025\"><!-- ################## --><\/p>\n<p>20\uc138\uae30 \ucd08 \ud790\ubca0\ub974\ud2b8\ub294 \uc644\uc804\ud558\uace0 \ubb34\ubaa8\uc21c\uc778 \uacf5\ub9ac \uccb4\uacc4 \uc704\uc5d0 \uc218\ud559\uc758 \uc138\uacc4\ub97c \uac74\uc124\ud558\uace0\uc790 \ud558\ub294 \uc57c\uc2ec\ucc2c \uacc4\ud68d\uc744 \uc81c\uc2dc\ud588\ub2e4. \uadf8\ub7ec\ub098 1931\ub144 \uad34\ub378\uc740 \ubd88\uc644\uc804\uc131 \uc815\ub9ac\ub97c \ud1b5\ud574 \uc774\ub7ec\ud55c \uacc4\ud68d\uc774 \uadfc\ubcf8\uc801\uc73c\ub85c \ubd88\uac00\ub2a5\ud568\uc744 \ubcf4\uc600\ub2e4.<\/p>\n<p>\uad34\ub378\uc758 \ubd88\uc644\uc804\uc131 \uc815\ub9ac\ub294 \uc790\uc5f0\uc218\uc758 \uae30\ubcf8 \uc131\uc9c8\uc744 \ud3ec\ud568\ud558\ub294 \ucda9\ubd84\ud788 \uac15\ud55c \ud615\uc2dd \uccb4\uacc4\ub294 \uc644\uc804\ud560 \uc218 \uc5c6\ub2e4\ub294 \uac83\uc744 \ubcf4\uc5ec\uc900\ub2e4. \uc989, \uadf8\ub7ec\ud55c \uccb4\uacc4\uc5d0\ub294 \uc99d\uba85\ub3c4 \ubc18\uc99d\ub3c4 \ud560 \uc218 \uc5c6\ub294 \uba85\uc81c\uac00 \ubc18\ub4dc\uc2dc \uc874\uc7ac\ud55c\ub2e4. \ub354 \ub098\uc544\uac00 \uadf8\ub7ec\ud55c \uccb4\uacc4\uac00 \ubb34\ubaa8\uc21c\uc774\ub77c\uba74, \uc790\uae30 \uc790\uc2e0\uc758 \ubb34\ubaa8\uc21c\uc131\uc744 \uc99d\uba85\ud560 \uc218 \uc5c6\ub2e4\ub294 \ub180\ub77c\uc6b4 \uacb0\uacfc\ub3c4 \ub530\ub77c\uc628\ub2e4.<\/p>\n<p>\uc774 \ubd80\uc5d0\uc11c\ub294 \ud398\uc544\ub178 \uc0b0\uc220\uc774\ub77c\ub294 \uad6c\uccb4\uc801\uc778 \ud615\uc2dd \uccb4\uacc4\ub97c \ud1b5\ud574 \ubd88\uc644\uc804\uc131 \uc815\ub9ac\ub97c \uc0b4\ud3b4\ubcf8\ub2e4. \uad34\ub378\uc774 \uc0ac\uc6a9\ud55c \ub3c5\ucc3d\uc801\uc778 \ubc29\ubc95\uc778 \uad34\ub378 \uc218\ub9e4\uae40\uc744 \ub3c4\uc785\ud558\uace0, \uc774\ub97c \ud1b5\ud558\uc5ec \uad34\ub378\uc758 \ubd88\uc644\uc804\uc131 \uc815\ub9ac\uc758 \ud575\uc2ec \uc544\uc774\ub514\uc5b4\ub97c \uae30\uc220\ud55c\ub2e4. \ub610\ud55c \ubd88\uc644\uc804\uc131 \uc815\ub9ac\uc758 \ub300\ud45c\uc801\uc778 \uc608\uc778 \ub7a8\uc9c0 \uc815\ub9ac\uc640 \ud398\ub9ac\uc2a4-\ud574\ub9c1\uc2a4\ud134 \uc815\ub9ac\ub97c \uc0b4\ud3b4\ubcf8\ub2e4.<\/p>\n<p><!-- \n\n<h2>18. \ud398\uc544\ub178 \uc0b0\uc220<\/h2>\n\n --><\/p>\n<h3>\uc77c\uacc4\ub17c\ub9ac\uc758 \uc644\uc804\uc131\uacfc \uc774\ub860<\/h3>\n<p>\uc77c\uacc4\ub17c\ub9ac \ubb38\uc7a5\uc758 \uc9d1\ud569 \\(\\varSigma\\)\uac00 <span class=\"defined\">\uc644\uc804\ud558\ub2e4<\/span>(complete)\ub294 \uac83\uc740 \uc784\uc758\uc758 \ubb38\uc7a5 \\(\\alpha\\)\uc5d0 \ub300\ud558\uc5ec \\(\\alpha\\) \ub610\ub294 \\((\\lnot \\alpha)\\) \uc911 \ud558\ub098\uac00 \\(\\varSigma\\)\uc758 \ub17c\ub9ac\uc801 \uadc0\uacb0\uc778 \uac83\uc774\ub2e4. \uc77c\uacc4\ub17c\ub9ac\uc758 \uc644\uc804\uc131 \uc815\ub9ac\uc5d0\uc11c\ub294 \ud615\uc2dd\uacc4\uc758 \uc644\uc804\uc131\uc744 \ub9d0\ud558\uae30 \ub54c\ubb38\uc5d0 \uc6a9\uc5b4\uc758 \uc0ac\uc6a9\uc774 \uc57d\uac04 \ub2e4\ub974\uc9c0\ub9cc, \ub450 \uac1c\ub150\uc740 \uae4a\uc740 \uc5f0\uad00\uc774 \uc788\ub2e4. \\(\\varSigma\\)\uac00 \uc644\uc804\ud560 \ub54c\ub294 \uc784\uc758\uc758 \ubb38\uc7a5 \\(\\alpha\\)\uc5d0 \ub300\ud558\uc5ec \\(\\alpha\\) \ub610\ub294 \\((\\lnot \\alpha)\\)\uac00 \\(\\varSigma\\)\ub85c\ubd80\ud130 \uc99d\uba85\ub420 \uc218 \uc788\uae30 \ub54c\ubb38\uc774\ub2e4.<\/p>\n<p>\\(M\\)\uc774 \uad6c\uc870\uc77c \ub54c, \\(M \\models \\sigma\\)\uc778 \ubaa8\ub4e0 \\(\\sigma\\)\ub4e4\uc758 \ubaa8\uc784, \uc989 \\(M\\)\uc5d0\uc11c \uc131\ub9bd\ud558\ub294 \ubaa8\ub4e0 \uc77c\uacc4\ub17c\ub9ac \ubb38\uc7a5 \\(\\sigma\\)\ub4e4\uc758 \ubaa8\uc784\uc744 \\(M\\)\uc758 <span class=\"defined\">\uc774\ub860<\/span>(theory)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. \\(M\\)\uc758 \uc774\ub860\uc740 \uc644\uc804\uc131\uc744 \uac00\uc9c4\ub2e4.<\/p>\n<p>\ubb38\uc7a5\ub4e4\uc758 \ubaa8\uc784 \\(\\varSigma\\)\uac00 \ubb34\ud55c \ubaa8\ub378\uc744 \uac00\uc9c0\uba74 \\(\\varSigma\\)\ub294 \uc5ec\ub7ec \uac1c\uc758 \ubaa8\ub378\uc744 \uac00\uc9c4\ub2e4. \uadf8\ub7ec\ub098 \ub9cc\uc57d \\(\\varSigma\\)\uac00 \uc644\uc804\uc131\uc744 \uac00\uc9c0\uba74 \\(\\varSigma\\)\uc758 \ubaa8\ub378\uc740 \ubaa8\ub450 \ub3d9\uc77c\ud55c \uc77c\uacc4\ub17c\ub9ac \uc774\ub860\uc744 \uac00\uc9c4\ub2e4.<\/p>\n<p>\uc218\ud559\uc758 \ud2b9\uc815 \ubd84\uc57c\ub97c \uacf5\ub9ac\ud654\ud55c\ub2e4\uace0 \ud560 \ub54c, \uadf8 \ubd84\uc57c\uac00 \uad70\ub860\uacfc \uac19\uc774 \ub2e4\uc591\ud55c \ubaa8\ub378\uc744 \uac00\uc9c0\ub294 \uacbd\uc6b0\uc5d0\ub294 \uc644\uc804\ud55c \ud558\ub098\uc758 \uc9d1\ud569\uc744 \uc815\ud558\ub824\uace0 \ud558\uc9c0\ub294 \uc54a\ub294\ub2e4. \ubc18\uba74, \ud558\ub098\uc758 \ubaa8\ub378\ub9cc\uc744 \uac16\ub294 \ubd84\uc57c\ub97c \uacf5\ub9ac\ud654\ud55c\ub2e4\uba74 \uc77c\uacc4\ub17c\ub9ac\uc758 \ubb38\uc7a5\uc744 \uc801\uc808\ud788 \uad6c\uc131\ud558\uc5ec \uadf8 \ubb38\uc7a5\ub4e4\uc774 \ubaa8\ub378\uc744 \uc644\uc804\ud788 \uacb0\uc815\ud558\ub3c4\ub85d \ud574\uc57c \ud55c\ub2e4.<\/p>\n<h3>\uc790\uc5f0\uc218\uacc4<\/h3>\n<p>\uc77c\uacc4\ub17c\ub9ac\ub97c \uc0ac\uc6a9\ud558\uc5ec \uacf5\ub9ac\ud654\ud560 \ub54c \ud765\ubbf8\ub85c\uc6b4 \ubd84\uc57c\uac00 \ubc14\ub85c \uc790\uc5f0\uc218\uacc4\uc774\ub2e4. \uc5ec\uae30\uc11c\ub294 \uc790\uc5f0\uc218 \uc9d1\ud569\uc744 \\(0\\) \uc774\uc0c1\uc758 \uc815\uc218\uc758 \uc9d1\ud569\uc73c\ub85c \uc815\uc758\ud558\uace0 \\(\\omega\\)\ub85c \ub098\ud0c0\ub0b4\uae30\ub85c \ud558\uc790.<\/p>\n<p>\uc9d1\ud569\ub860\uc744 \uad6c\uc131\ud558\uc9c0 \uc54a\uace0 \\(\\omega\\)\uc758 \uad6c\uc870\ub97c \uc77c\uacc4\ub17c\ub9ac\ub85c \uc9c1\uc811 \uacf5\ub9ac\ud654\ud558\ub294 \uac83\uc774 \uac00\ub2a5\ud560\uae4c? \uc77c\uacc4\ub17c\ub9ac\ub97c \uc0ac\uc6a9\ud55c \\(\\omega\\)\uc758 \uacf5\ub9ac\ub294 \\(0\\)\uc73c\ub85c\ubd80\ud130 \ucd9c\ubc1c\ud558\uc5ec \ub530\ub984\uc218(successor)\ub97c \ucde8\ud568\uc73c\ub85c\uc368 \\(\\omega\\)\uc758 \ubaa8\ub4e0 \uc6d0\uc18c\ub97c \uc5bb\uc744 \uc218 \uc788\uc5b4\uc57c \ud55c\ub2e4. \uadf8\ub7ec\ub098 \uc77c\uacc4\ub17c\ub9ac\ub9cc\uc73c\ub85c\ub294 &#8216;\uc784\uc758\uc758 \uc720\ud55c \ubc88\uc758 \ubc18\ubcf5&#8217;\uc5d0 \ub300\ud558\uc5ec \ub17c\ud560 \uc218 \uc5c6\ub2e4. \uadf8\ub7ec\ud55c \ud45c\ud604\uc774 \uc77c\uacc4\ub17c\ub9ac\uc5d0\uc11c \ud5c8\uc6a9\ub418\uc9c0 \uc54a\uae30 \ub54c\ubb38\uc774\ub2e4.<\/p>\n<p>\\(\\omega\\)\ub294 \uc790\uae30\ub3d9\ud615\uc0ac\uc0c1\uc744 \uac16\uc9c0 \uc54a\ub294\ub2e4. [\\(\\omega\\)\uc758 \uc790\uae30\ub3d9\ud615\uc0ac\uc0c1\uc740 \\(0\\)\uc744 \ubd80\ub3d9\uc810\uc73c\ub85c \uac16\uace0, \uadf8\uc5d0 \ub530\ub77c \\(1,\\) \\(2,\\) \\(3,\\) \\(\\cdots\\)\ub3c4 \ubd80\ub3d9\uc810\uc73c\ub85c \uac00\uc9c4\ub2e4. \ub530\ub77c\uc11c \\(\\omega\\)\ub294 \uc62c\ub9ac\uace0\ubaa8\ub974\ud53d \uad70(oligomorphic group)\uc774 \uc544\ub2c8\uba70 \\(\\omega\\)\uc640 \ub3d9\ud615\uc774 \uc544\ub2cc \uac00\uc0b0 \ubaa8\ub378\uc744 \uac00\uc9c4\ub2e4.] \ub530\ub77c\uc11c \\(\\omega\\)\ub97c \uacf5\ub9ac\ud654\ud560 \ub54c\uc5d0\ub294 \ubaa8\ub378\uc758 \uc720\uc77c\uc131\uc744 \uae30\ub300\ud560 \uc218 \uc5c6\uc73c\uba70, \\(\\omega\\)\uc758 \uc131\uc9c8\uc744 \ubaa8\ub450 \ub04c\uc5b4\ub0bc \uc218 \uc788\ub294 \uc644\uc804\uc131\uc744 \uac16\ub294 \ub2e8\uc21c\ud55c \uacf5\ub9ac\uacc4\ub97c \uad6c\uc131\ud558\ub294 \uac83\uc774 \ucd5c\uc120\uc774\ub2e4.<\/p>\n<p>\ub530\ub984\uc218 \uc6d0\ub9ac(succession principle)\ub294 \uc218\ud559\uc801 \uadc0\ub0a9\ubc95\uc758 \uadfc\uac70\uac00 \ub418\uba70, \uc774\uac83\uc744 \uad6c\ud604\ud558\ub294 \ubc29\ubc95\uc740 \uc218\ud559\uc801 \uadc0\ub0a9\ubc95\uc758 \uc6d0\ub9ac(principle of induction)\ub97c \ud5c8\uc6a9\ud558\ub294 \uac83\uc774\ub2e4. \uc131\uc9c8 \\(\\mathrm{P}\\)\uac00 \\(0\\)\uc5d0 \ub300\ud558\uc5ec \uc131\ub9bd\ud558\uace0, \\(\\mathrm{P}\\)\uac00 \\(n\\)\uc5d0 \ub300\ud558\uc5ec \uc131\ub9bd\ud560 \ub54c\ub9c8\ub2e4 \\(n+1\\)\uc5d0 \ub300\ud574\uc11c\ub3c4 \uc131\ub9bd\ud558\uba74, \\(\\mathrm{P}\\)\ub294 \uc784\uc758\uc758 \\(n \\in \\omega\\)\uc5d0 \ub300\ud558\uc5ec \uc131\ub9bd\ud574\uc57c \ud55c\ub2e4. \uadf8\ub7ec\ub098 \uc77c\uacc4\ub17c\ub9ac\uc5d0\uc11c\ub294 \uc77c\uacc4\ub17c\ub9ac\uc2dd\uc73c\ub85c \ud45c\ud604 \uac00\ub2a5\ud55c \uc131\uc9c8\ub9cc \ub2e4\ub8f0 \uc218 \uc788\ub2e4.<\/p>\n<h3>\uc790\uc5f0\uc218\uacc4\uc758 \uacf5\ub9ac\ud654<\/h3>\n<p>\\(\\omega\\)\ub97c \uacf5\ub9ac\ud654\ud558\uae30 \uc704\ud558\uc5ec \uba3c\uc800 \ub530\ub984\uc218 \ud568\uc218(successor function)\uc640 \uad00\ub828\ub41c \uacf5\ub9ac\ub97c \ub3c4\uc785\ud558\uc790. \uc6b0\ub9ac\uc758 \uc5b8\uc5b4\ub294 \uc0c1\uc218\uae30\ud638 \\(0\\)\uacfc \uc77c\ud56d\ud568\uc218 \\(s\\)\ub97c \uac00\uc9c0\ub294 \uac83\uc73c\ub85c \uc57d\uc18d\ud55c\ub2e4. \uc5ec\uae30\uc11c \\(s\\)\ub294 \ub530\ub984\uc218 \ud568\uc218\ub97c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\n<ul>\n<li>(P1) \\(0\\)\uc744 \uc81c\uc678\ud55c \uc784\uc758\uc758 \uc6d0\uc18c \\(x\\)\ub294 \uc720\uc77c\ud55c \\(y\\)\uc758 \ub530\ub984\uc218\uc774\ub2e4.<\/li>\n<li>(P2) \\(0\\)\uc740 \uc5b4\ub5a0\ud55c \uc6d0\uc18c\uc758 \ub530\ub984\uc218\ub3c4 \uc544\ub2c8\ub2e4.<\/li>\n<\/ul>\n<p>\uc774\ub4e4 \uacf5\ub9ac\ub294 \uc77c\uacc4\ub17c\ub9ac\uc758 \ubb38\uc7a5\uc73c\ub85c \ud45c\ud604\ub41c\ub2e4. \uc608\ub97c \ub4e4\uc5b4 (P2)\ub294 \\((\\forall x)(\\lnot (s(x) =0))\\)\uc73c\ub85c \ud45c\ud604\ub41c\ub2e4. (P1)\uacfc (P2)\ub294 \uc11c\ub85c \ub3d9\ud615\uc774 \uc544\ub2cc \uac00\uc0b0 \ubaa8\ub378\uc744 \ubb34\ud55c\ud788 \ub9ce\uc774 \uac00\uc9c4\ub2e4.<\/p>\n<p>\uc774\uc81c \ub367\uc148\uacfc \uacf1\uc148\uc744 \ub2e4\ub8f0 \uc218 \uc788\ub294 \uacf5\ub9ac\ub97c \ucd94\uac00\ud558\uc790.<\/p>\n<ul>\n<li>(P3) \\((\\forall x)(x+0=x)\\)<\/li>\n<li>(P4) \\((\\forall x)(\\forall y)(x+s(y) = s(x+y))\\)<\/li>\n<li>(P5) \\((\\forall x)(x \\cdot 0 =0)\\)<\/li>\n<li>(P6) \\((\\forall x)(\\forall y)(x \\cdot s(y) = x \\cdot y + x)\\)<\/li>\n<\/ul>\n<p>\ub05d\uc73c\ub85c \uc218\ud559\uc801 \uadc0\ub0a9\ubc95\uc758 \uc6d0\ub9ac\ub97c \uc704\ud55c \uacf5\ub9ac\ub97c \ub3c4\uc785\ud558\uc790. \uc774 \uacf5\ub9ac\ub294 \ud558\ub098\uc758 \uacf5\ub9ac\uac00 \uc544\ub2cc \uacf5\ub9ac\ud2c0\uc774\ub2e4. \uc989 \ud558\ub098\uc758 \uc790\uc720\ubcc0\uc218 \\(x\\)\ub97c \uac00\uc9c4 \uc5b8\uc5b4\uc758 \uac01 \ub17c\ub9ac\uc2dd \\(\\phi\\)\uc5d0 \ub300\ud558\uc5ec \uacf5\ub9ac\uac00 \ud558\ub098\uc529 \ub300\uc751\ub41c\ub2e4.<\/p>\n<ul>\n<li>(P7) \\(((\\phi [0\/x] \\wedge (\\forall x)(\\phi \\rightarrow \\phi [s(x)\/x])) \\rightarrow (\\forall x)\\phi)\\)<\/li>\n<\/ul>\n<p>(P1)\\(\\sim\\)(P7)\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uacf5\ub9ac\uacc4\ub97c <span class=\"defined\">\ud398\uc544\ub178 \uc0b0\uc220<\/span>(Peano arithmetic)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. [\ucc38\uace0\ub85c \ud398\uc544\ub178 \uc0b0\uc220\uc740 \\(\\omega\\) \ubfd0\ub9cc \uc544\ub2c8\ub77c \\(\\omega\\)\uc640\ub294 \ub2e4\ub978 \ubaa8\ub378\ub3c4 \uac00\uc9c4\ub2e4. \uadf8\ub7ec\ud55c \ubaa8\ub378\uc744 &#8216;\ube44\ud45c\uc900 \ubaa8\ub378&#8217;\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.]<\/p>\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>20\uc138\uae30 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