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List of mathematical logic topics

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1025: 982: 854: 820: 716: 668: 622: 467: 441: 431: 285: 226: 221: 17: 2750: 2476: 2471: 2261: 2251: 2095: 1984: 1922: 1890: 1836: 1831: 1710: 1641: 1385: 1320: 1179: 1005: 975: 869: 796: 692: 658: 648: 595: 436: 414: 363: 280: 179: 167: 103: 1311: 2596: 2538: 2373: 2162: 2075: 2009: 1954: 1949: 1841: 1826: 1791: 1715: 1691: 1619: 1584: 1574: 1569: 1554: 1549: 1481: 1392: 1353: 1330: 1139: 1009: 888: 881: 590: 548: 426: 268: 241: 130: 909: 2850: 2543: 2522: 2437: 2424: 2343: 2053: 1989: 1964: 1895: 1686: 1559: 1539: 1339: 1276: 1230: 1216: 1146: 1016: 996: 825: 307: 162: 150: 79: 2880: 2700: 2641: 2419: 2414: 1927: 1907: 1885: 1781: 1519: 1290: 1076: 801: 617: 419: 258: 184: 145: 2690: 2512: 2333: 2043: 2026: 1132: 1090: 979: 731: 632: 558: 358: 194: 172: 74: 2725: 2720: 2673: 2385: 2338: 2199: 2157: 1917: 1868: 1700: 1676: 1439: 1176: 1002: 972: 612: 543: 526: 2668: 2636: 2601: 2396: 1478: 1350: 1327: 986: 637: 395: 113: 2730: 2591: 2502: 2036: 1912: 1666: 1661: 1336: 1258: 1227: 1213: 993: 373: 140: 135: 62: 2651: 2229: 2204: 2070: 766: 2715: 2646: 2360: 1979: 2553: 2065: 1436: 849: 2745: 2460: 2705: 1255: 1183: 2433: 2429: 2865: 2794: 2766: 2759: 2614: 2579: 2531: 2485: 478:Original proof of Gödel's completeness theorem 379:Elementary Calculus: An Infinitesimal Approach 2445: 8: 59:list of computability and complexity topics 53:For traditional syllogistic logic, see the 2763: 2528: 2452: 2438: 2430: 1372:Kripke–Platek set theory with urelements 1430:Simple theorems in the algebra of sets 126:Simple theorems in the algebra of sets 325:Tarski's exponential function problem 7: 2627:Analytic and synthetic propositions 2498:Formal semantics (natural language) 952:Cantor's first uncountability proof 2381:Systems of Logic Based on Ordinals 1787:Effective results in number theory 966:Cantor–Bernstein–Schroeder theorem 384:Criticism of non-standard analysis 25: 2897:Outlines of mathematics and logic 539:Atomic model (mathematical logic) 2839: 2399: 737:Non-standard model of arithmetic 1960:Tarski's undefinability theorem 1822:Computational complexity theory 1755:Recursively enumerable language 1198:Axiom of projective determinacy 502:Gödel's incompleteness theorems 1600:Totally indescribable cardinal 1580:Strongly inaccessible cardinal 938:Cantor's back-and-forth method 507:Structure (mathematical logic) 342:Institution (computer science) 1: 1451:Tree (descriptive set theory) 831:Interpretation (model theory) 703:Strength (mathematical logic) 603:Morley's categoricity theorem 303:Descriptive complexity theory 18:Outline of mathematical logic 2240:Luitzen Egbertus Jan Brouwer 2210:Introduction to topos theory 2175:Simply typed lambda calculus 1672:Primitive recursive function 1615:Weakly inaccessible cardinal 1610:Weakly hyper-Woodin cardinal 683:List of first-order theories 473:Gödel's completeness theorem 2289:E equational theorem prover 2132:Mathematical constructivism 2081:Gentzen's consistency proof 2032:Intuitionistic linear logic 1842:Complexity classes P and NP 1738:Post correspondence problem 1407:Zermelo–Fraenkel set theory 1161:Uniformization (set theory) 919:Boolean algebra (structure) 777:Barwise compactness theorem 712:Differentially closed field 586:Theory (mathematical logic) 232:Arithmetization of analysis 2923: 2153:Intuitionistic type theory 1852:List of complexity classes 1750:Recursively enumerable set 1745:Kleene's recursion theorem 1168:Universally measurable set 1105:Borel equivalence relation 945:Cantor's diagonal argument 840:Pregeometry (model theory) 654:Weakly o-minimal structure 554:Existentially closed model 517:Substructure (mathematics) 337:Institutional model theory 237:Foundations of mathematics 28: 2887:Mathematics-related lists 2834: 2711:Necessity and sufficiency 2467: 2279:Automated theorem proving 2225:Computable measure theory 2190:Calculus of constructions 2061:Proof-theoretic semantics 1726:Calculus of constructions 1284:Infinite descending chain 1242:Intersection (set theory) 1205:Axiom of real determinacy 903:Axiom of dependent choice 896:Axiom of countable choice 787:Lindenbaum–Tarski algebra 2329:Interactive proof system 2185:Curry–Howard isomorphism 1047:Complete Boolean algebra 807:Ehrenfeucht–FraĂŻssĂ© game 490:Löwenheim–Skolem theorem 2356:Automated Mathematician 2304:Isabelle theorem prover 2195:Constructivist analysis 2000:Self-verifying theories 1995:Structural proof theory 1879:Space hierarchy theorem 1802:Word problem for groups 1605:Weakly compact cardinal 1379:Morse–Kelley set theory 1263:Large cardinal property 1119:Lightface analytic game 1040:Complement (set theory) 835:Interpretable structure 812:Herbrand interpretation 747:Second-order arithmetic 722:Ax–Grothendieck theorem 628:Strongly minimal theory 574:Hrushovski construction 522:Elementary substructure 320:Computable model theory 274:Boolean algebra (logic) 121:Singleton (mathematics) 55:list of topics in logic 2324:Vampire theorem prover 2319:Paradox theorem prover 2294:Gandalf theorem prover 2274:First-order resolution 2215:LF (logical framework) 2091:Nonfirstorderizability 1975:Interpretability logic 1874:Time hierarchy theorem 1807:Arithmetical hierarchy 1797:Matiyasevich's theorem 1505:Almost Ramsey cardinal 1487:Descriptive set theory 1358:Alternative set theory 1084:Descriptive set theory 1054:Continuum (set theory) 845:Quantifier elimination 742:First-order arithmetic 698:Pseudoelementary class 688:Conservative extension 512:Interpretation (logic) 389:Standard part function 313:Trakhtenbrot's theorem 158:Universe (mathematics) 87:Mathematical induction 2846:Philosophy portal 2180:Typed lambda calculus 2168:Church–Rosser theorem 2138:Nonconstructive proof 2101:Weak interpretability 1938:Definable real number 1862:Exponential hierarchy 1817:Presburger arithmetic 1721:Church-Rosser theorem 1590:Supercompact cardinal 1530:Inaccessible cardinal 1525:Hyper-Woodin cardinal 1305:Transfinite induction 1221:Forcing (mathematics) 772:Back-and-forth method 752:Presburger arithmetic 678:Model complete theory 581:Potential isomorphism 569:Amalgamation property 401:Forcing (mathematics) 354:Non-standard calculus 349:Non-standard analysis 264:Definable real number 248:Principia Mathematica 215:Nonconstructive proof 109:Element (mathematics) 2314:Otter theorem prover 2148:Intuitionistic logic 2005:Substructural logics 1857:Polynomial hierarchy 1767:Undecidable language 1697:Computability theory 1652:Church–Turing thesis 1647:Decidability (logic) 1637:Entscheidungsproblem 1595:Superstrong cardinal 1493:Analytical hierarchy 1472:Von Neumann universe 1365:Axiomatic set theory 1191:Axiom of determinacy 1126:Perfect set property 1098:Analytical hierarchy 1070:Continuum hypothesis 931:Burali-Forti paradox 924:Boolean-valued model 762:Functional predicate 664:Spectrum of a theory 454:Lindström quantifier 406:Boolean-valued model 200:Reductio ad absurdum 97:Recursive definition 92:Structural induction 2508:Philosophy of logic 2284:ACL2 theorem prover 2220:Computability logic 2116:Cotolerant sequence 2086:Reverse mathematics 1933:Stephen Cole Kleene 1812:Subrecursion theory 1657:Computable function 1625:Unfoldable cardinal 1565:Remarkable cardinal 1545:Measurable cardinal 1515:Extendible cardinal 1400:Positive set theory 1235:Internal set theory 865:Type (model theory) 485:Compactness theorem 330:Undecidable problem 298:Finite model theory 205:Proof by exhaustion 69:Working foundations 61:for more theory of 2892:Mathematical logic 2807:Rules of inference 2776:Mathematical logic 2518:Semantics of logic 2309:LCF theorem prover 2299:HOL theorem prover 2106:Cointerpretability 1762:Decidable language 1682:Ackermann function 1535:Ineffable cardinal 1465:Union (set theory) 1414:Zermelo set theory 1270:Musical set theory 1112:Infinity-Borel set 1033:Class (set theory) 860:Skolem normal form 816:Herbrand structure 608:Stability spectrum 564:Age (model theory) 534:Non-standard model 459:Second-order logic 449:Higher-order logic 369:Transfer principle 210:Constructive proof 190:Mathematical proof 46:mathematical logic 2874: 2873: 2830: 2829: 2664:Deductive closure 2610: 2609: 2549:Critical thinking 2407:Philosophy portal 2350:Discovery systems 2257:Sahlqvist formula 2235:Ultraintuitionism 2143:Existence theorem 2126:Cirquent calculus 2121:Deduction theorem 2111:Tolerant sequence 1970:Provability logic 1733:Combinatory logic 1706:Herbrand Universe 1458:Tree (set theory) 1423:Set (mathematics) 1344:Russell's paradox 1298:Successor ordinal 1154:Property of Baire 1026:Cartesian product 855:Signature (logic) 821:Imaginary element 727:Ax–Kochen theorem 717:Exponential field 669:Vaught conjecture 623:Forking extension 468:Soundness theorem 442:Many-sorted logic 432:First-order logic 286:categorical logic 254:Hilbert's program 227:Consistency proof 16:(Redirected from 2914: 2844: 2843: 2842: 2764: 2529: 2493:Computer science 2454: 2447: 2440: 2431: 2409: 2404: 2403: 2402: 2262:Interior algebra 2252:Kripke semantics 2096:Interpretability 1985:Sequent calculus 1923:Jacques Herbrand 1891:Hypercomputation 1837:Complexity class 1832:Exponential time 1711:Markov algorithm 1642:Decision problem 1631:Recursion theory 1386:Naive set theory 1321:Well-founded set 1061:Suslin's problem 959:Cantor's theorem 870:Zariski geometry 797:Arithmetical set 757:Wilkie's theorem 693:Elementary class 659:C-minimal theory 649:o-minimal theory 495:Skolem's paradox 437:Infinitary logic 415:Kripke semantics 364:Hyperreal number 281:Dialectica space 180:Axiomatic method 168:Axiomatic system 104:Naive set theory 21: 2922: 2921: 2917: 2916: 2915: 2913: 2912: 2911: 2907:Lists of topics 2877: 2876: 2875: 2870: 2840: 2838: 2826: 2790: 2781:Boolean algebra 2755: 2606: 2597:Metamathematics 2575: 2527: 2481: 2463: 2458: 2405: 2400: 2398: 2395: 2374:Begriffsschrift 2369: 2352: 2270: 2268:Theorem provers 2248: 2163:Lambda calculus 2134: 2076:Gerhard Gentzen 2010:Structural rule 1955:Cut-elimination 1950:Metamathematics 1946: 1827:Polynomial time 1792:Diophantine set 1716:Lambda calculus 1692:Halting problem 1633: 1620:Woodin cardinal 1585:Subtle cardinal 1575:Strong cardinal 1570:Shelah cardinal 1555:Ramsey cardinal 1550:N-huge cardinal 1501: 1499:Large cardinals 1489: 1393:New Foundations 1140:Prewellordering 1010:Cardinal number 889:Axiom of choice 882:Algebra of sets 878: 591:Complete theory 549:Saturated model 427:Predicate logic 294: 269:Algebraic logic 242:Formal language 131:Algebra of sets 71: 57:. See also the 40: 37:related changes 32:related changes 23: 22: 15: 12: 11: 5: 2920: 2918: 2910: 2909: 2904: 2899: 2894: 2889: 2879: 2878: 2872: 2871: 2869: 2868: 2863: 2853: 2848: 2835: 2832: 2831: 2828: 2827: 2825: 2824: 2819: 2814: 2809: 2804: 2798: 2796: 2792: 2791: 2789: 2788: 2783: 2778: 2772: 2770: 2761: 2757: 2756: 2754: 2753: 2748: 2743: 2738: 2733: 2728: 2723: 2718: 2713: 2708: 2703: 2698: 2693: 2688: 2687: 2686: 2676: 2671: 2666: 2661: 2656: 2655: 2654: 2649: 2639: 2634: 2629: 2624: 2618: 2616: 2612: 2611: 2608: 2607: 2605: 2604: 2599: 2594: 2589: 2583: 2581: 2577: 2576: 2574: 2573: 2568: 2563: 2558: 2557: 2556: 2551: 2541: 2535: 2533: 2526: 2525: 2520: 2515: 2510: 2505: 2500: 2495: 2489: 2487: 2483: 2482: 2480: 2479: 2474: 2468: 2465: 2464: 2459: 2457: 2456: 2449: 2442: 2434: 2428: 2427: 2425:Saharon Shelah 2422: 2417: 2411: 2410: 2394: 2391: 2390: 2389: 2377: 2368: 2365: 2364: 2363: 2358: 2351: 2348: 2347: 2346: 2341: 2336: 2331: 2326: 2321: 2316: 2311: 2306: 2301: 2296: 2291: 2286: 2281: 2276: 2269: 2266: 2265: 2264: 2259: 2254: 2247: 2244: 2243: 2242: 2237: 2232: 2227: 2222: 2217: 2212: 2207: 2202: 2197: 2192: 2187: 2182: 2177: 2172: 2171: 2170: 2160: 2155: 2150: 2145: 2140: 2133: 2130: 2129: 2128: 2123: 2118: 2113: 2108: 2103: 2098: 2093: 2088: 2083: 2078: 2073: 2068: 2063: 2058: 2057: 2056: 2054:Relevant logic 2051: 2046: 2041: 2040: 2039: 2034: 2024: 2023: 2022: 2017: 2002: 1997: 1992: 1990:Analytic proof 1987: 1982: 1977: 1972: 1967: 1965:Diagonal lemma 1962: 1957: 1952: 1945: 1942: 1941: 1940: 1935: 1930: 1925: 1920: 1915: 1910: 1905: 1900: 1899: 1898: 1896:Oracle machine 1888: 1883: 1882: 1881: 1876: 1871: 1866: 1865: 1864: 1859: 1854: 1849: 1847:Cook's theorem 1844: 1834: 1829: 1824: 1819: 1809: 1804: 1799: 1794: 1789: 1784: 1779: 1777:Post's theorem 1774: 1772:Rice's theorem 1769: 1764: 1759: 1758: 1757: 1747: 1742: 1741: 1740: 1735: 1730: 1729: 1728: 1723: 1713: 1708: 1703: 1694: 1689: 1687:Turing machine 1684: 1679: 1674: 1669: 1664: 1654: 1649: 1644: 1639: 1632: 1629: 1628: 1627: 1622: 1617: 1612: 1607: 1602: 1597: 1592: 1587: 1582: 1577: 1572: 1567: 1562: 1560:Rank-into-rank 1557: 1552: 1547: 1542: 1540:Mahlo cardinal 1537: 1532: 1527: 1522: 1517: 1512: 1510:ErdƑs cardinal 1507: 1500: 1497: 1496: 1495: 1488: 1485: 1484: 1483: 1476: 1469: 1462: 1455: 1448: 1444:Θ (set theory) 1441: 1434: 1427: 1420: 1419: 1418: 1411: 1404: 1397: 1390: 1383: 1376: 1369: 1362: 1348: 1341: 1334: 1333: 1332: 1325: 1318: 1317: 1316: 1302: 1295: 1288: 1277:Ordinal number 1274: 1267: 1260: 1253: 1246: 1239: 1232: 1225: 1218: 1211: 1210: 1209: 1202: 1195: 1188: 1174: 1173: 1172: 1165: 1158: 1151: 1147:Projective set 1144: 1137: 1130: 1123: 1116: 1109: 1102: 1095: 1081: 1074: 1067: 1066: 1065: 1051: 1044: 1037: 1030: 1023: 1022: 1021: 1017:Hartogs number 1014: 1007: 1000: 999: 998: 991: 970: 963: 956: 949: 942: 935: 928: 921: 916: 915: 914: 907: 900: 886: 877: 874: 873: 872: 867: 862: 857: 852: 847: 842: 837: 828: 826:Indiscernibles 823: 818: 809: 804: 799: 794: 789: 784: 779: 774: 769: 764: 759: 754: 749: 744: 739: 734: 729: 724: 719: 714: 709: 708: 707: 706: 705: 700: 690: 685: 680: 675: 674: 673: 672: 671: 661: 656: 651: 646: 645: 644: 643: 642: 641: 640: 630: 625: 615: 600: 599: 598: 583: 578: 577: 576: 571: 561: 556: 551: 546: 541: 536: 531: 530: 529: 519: 514: 509: 504: 499: 498: 497: 487: 482: 481: 480: 470: 465: 464: 463: 462: 461: 456: 446: 445: 444: 439: 424: 423: 422: 412: 411: 410: 409: 408: 393: 392: 391: 386: 381: 376: 371: 366: 361: 356: 346: 345: 344: 334: 333: 332: 327: 317: 316: 315: 310: 308:Model checking 305: 293: 290: 289: 288: 283: 278: 277: 276: 266: 261: 256: 251: 244: 239: 234: 229: 224: 219: 218: 217: 212: 207: 202: 197: 187: 182: 177: 176: 175: 165: 163:Axiomatization 160: 155: 154: 153: 151:Empty function 148: 143: 138: 133: 128: 123: 118: 117: 116: 101: 100: 99: 94: 84: 83: 82: 80:Giuseppe Peano 70: 67: 24: 14: 13: 10: 9: 6: 4: 3: 2: 2919: 2908: 2905: 2903: 2900: 2898: 2895: 2893: 2890: 2888: 2885: 2884: 2882: 2867: 2864: 2861: 2857: 2854: 2852: 2849: 2847: 2837: 2836: 2833: 2823: 2822:Logic symbols 2820: 2818: 2815: 2813: 2810: 2808: 2805: 2803: 2800: 2799: 2797: 2793: 2787: 2784: 2782: 2779: 2777: 2774: 2773: 2771: 2769: 2765: 2762: 2758: 2752: 2749: 2747: 2744: 2742: 2739: 2737: 2734: 2732: 2729: 2727: 2724: 2722: 2719: 2717: 2714: 2712: 2709: 2707: 2704: 2702: 2701:Logical truth 2699: 2697: 2694: 2692: 2689: 2685: 2682: 2681: 2680: 2677: 2675: 2672: 2670: 2667: 2665: 2662: 2660: 2657: 2653: 2650: 2648: 2645: 2644: 2643: 2642:Contradiction 2640: 2638: 2635: 2633: 2630: 2628: 2625: 2623: 2620: 2619: 2617: 2613: 2603: 2600: 2598: 2595: 2593: 2590: 2588: 2587:Argumentation 2585: 2584: 2582: 2578: 2572: 2571:Philosophical 2569: 2567: 2566:Non-classical 2564: 2562: 2559: 2555: 2552: 2550: 2547: 2546: 2545: 2542: 2540: 2537: 2536: 2534: 2530: 2524: 2521: 2519: 2516: 2514: 2511: 2509: 2506: 2504: 2501: 2499: 2496: 2494: 2491: 2490: 2488: 2484: 2478: 2475: 2473: 2470: 2469: 2466: 2462: 2455: 2450: 2448: 2443: 2441: 2436: 2435: 2432: 2426: 2423: 2421: 2420:Alfred Tarski 2418: 2416: 2413: 2412: 2408: 2397: 2392: 2387: 2386:Alan Turing's 2383: 2382: 2378: 2376: 2375: 2371: 2370: 2366: 2362: 2359: 2357: 2354: 2353: 2349: 2345: 2342: 2340: 2337: 2335: 2332: 2330: 2327: 2325: 2322: 2320: 2317: 2315: 2312: 2310: 2307: 2305: 2302: 2300: 2297: 2295: 2292: 2290: 2287: 2285: 2282: 2280: 2277: 2275: 2272: 2271: 2267: 2263: 2260: 2258: 2255: 2253: 2250: 2249: 2245: 2241: 2238: 2236: 2233: 2231: 2228: 2226: 2223: 2221: 2218: 2216: 2213: 2211: 2208: 2206: 2203: 2201: 2198: 2196: 2193: 2191: 2188: 2186: 2183: 2181: 2178: 2176: 2173: 2169: 2166: 2165: 2164: 2161: 2159: 2156: 2154: 2151: 2149: 2146: 2144: 2141: 2139: 2136: 2135: 2131: 2127: 2124: 2122: 2119: 2117: 2114: 2112: 2109: 2107: 2104: 2102: 2099: 2097: 2094: 2092: 2089: 2087: 2084: 2082: 2079: 2077: 2074: 2072: 2069: 2067: 2064: 2062: 2059: 2055: 2052: 2050: 2047: 2045: 2042: 2038: 2035: 2033: 2030: 2029: 2028: 2025: 2021: 2018: 2016: 2013: 2012: 2011: 2008: 2007: 2006: 2003: 2001: 1998: 1996: 1993: 1991: 1988: 1986: 1983: 1981: 1978: 1976: 1973: 1971: 1968: 1966: 1963: 1961: 1958: 1956: 1953: 1951: 1948: 1947: 1943: 1939: 1936: 1934: 1931: 1929: 1928:Haskell Curry 1926: 1924: 1921: 1919: 1916: 1914: 1911: 1909: 1908:Alonzo Church 1906: 1904: 1901: 1897: 1894: 1893: 1892: 1889: 1887: 1886:Natural proof 1884: 1880: 1877: 1875: 1872: 1870: 1867: 1863: 1860: 1858: 1855: 1853: 1850: 1848: 1845: 1843: 1840: 1839: 1838: 1835: 1833: 1830: 1828: 1825: 1823: 1820: 1818: 1815: 1814: 1813: 1810: 1808: 1805: 1803: 1800: 1798: 1795: 1793: 1790: 1788: 1785: 1783: 1782:Turing degree 1780: 1778: 1775: 1773: 1770: 1768: 1765: 1763: 1760: 1756: 1753: 1752: 1751: 1748: 1746: 1743: 1739: 1736: 1734: 1731: 1727: 1724: 1722: 1719: 1718: 1717: 1714: 1712: 1709: 1707: 1704: 1702: 1698: 1695: 1693: 1690: 1688: 1685: 1683: 1680: 1678: 1675: 1673: 1670: 1668: 1665: 1663: 1660: 1659: 1658: 1655: 1653: 1650: 1648: 1645: 1643: 1640: 1638: 1635: 1634: 1630: 1626: 1623: 1621: 1618: 1616: 1613: 1611: 1608: 1606: 1603: 1601: 1598: 1596: 1593: 1591: 1588: 1586: 1583: 1581: 1578: 1576: 1573: 1571: 1568: 1566: 1563: 1561: 1558: 1556: 1553: 1551: 1548: 1546: 1543: 1541: 1538: 1536: 1533: 1531: 1528: 1526: 1523: 1521: 1520:Huge cardinal 1518: 1516: 1513: 1511: 1508: 1506: 1503: 1502: 1498: 1494: 1491: 1490: 1486: 1482: 1480: 1477: 1475: 1473: 1470: 1468: 1466: 1463: 1461: 1459: 1456: 1454: 1452: 1449: 1447: 1445: 1442: 1440: 1438: 1435: 1433: 1431: 1428: 1426: 1424: 1421: 1417: 1415: 1412: 1410: 1408: 1405: 1403: 1401: 1398: 1396: 1394: 1391: 1389: 1387: 1384: 1382: 1380: 1377: 1375: 1373: 1370: 1368: 1366: 1363: 1361: 1359: 1356: 1355: 1354: 1352: 1349: 1347: 1345: 1342: 1340: 1338: 1335: 1331: 1329: 1326: 1324: 1322: 1319: 1315: 1313: 1310: 1309: 1308: 1306: 1303: 1301: 1299: 1296: 1294: 1292: 1291:Limit ordinal 1289: 1287: 1285: 1282: 1281: 1280: 1278: 1275: 1273: 1271: 1268: 1266: 1264: 1261: 1259: 1257: 1254: 1252: 1250: 1247: 1245: 1243: 1240: 1238: 1236: 1233: 1231: 1229: 1226: 1224: 1222: 1219: 1217: 1215: 1212: 1208: 1206: 1203: 1201: 1199: 1196: 1194: 1192: 1189: 1187: 1185: 1182: 1181: 1180: 1178: 1175: 1171: 1169: 1166: 1164: 1162: 1159: 1157: 1155: 1152: 1150: 1148: 1145: 1143: 1141: 1138: 1136: 1134: 1131: 1129: 1127: 1124: 1122: 1120: 1117: 1115: 1113: 1110: 1108: 1106: 1103: 1101: 1099: 1096: 1094: 1092: 1089: 1088: 1087: 1085: 1082: 1080: 1078: 1077:Countable set 1075: 1073: 1071: 1068: 1064: 1062: 1059: 1058: 1057: 1055: 1052: 1050: 1048: 1045: 1043: 1041: 1038: 1036: 1034: 1031: 1029: 1027: 1024: 1020: 1018: 1015: 1013: 1011: 1008: 1006: 1004: 1001: 997: 995: 992: 990: 988: 985: 984: 983: 981: 978: 977: 976: 974: 971: 969: 967: 964: 962: 960: 957: 955: 953: 950: 948: 946: 943: 941: 939: 936: 934: 932: 929: 927: 925: 922: 920: 917: 913: 911: 908: 906: 904: 901: 899: 897: 894: 893: 892: 890: 887: 885: 883: 880: 879: 875: 871: 868: 866: 863: 861: 858: 856: 853: 851: 848: 846: 843: 841: 838: 836: 832: 829: 827: 824: 822: 819: 817: 813: 810: 808: 805: 803: 802:Definable set 800: 798: 795: 793: 792:Löb's theorem 790: 788: 785: 783: 782:Skolemization 780: 778: 775: 773: 770: 768: 765: 763: 760: 758: 755: 753: 750: 748: 745: 743: 740: 738: 735: 733: 730: 728: 725: 723: 720: 718: 715: 713: 710: 704: 701: 699: 696: 695: 694: 691: 689: 686: 684: 681: 679: 676: 670: 667: 666: 665: 662: 660: 657: 655: 652: 650: 647: 639: 636: 635: 634: 631: 629: 626: 624: 621: 620: 619: 618:Stable theory 616: 614: 611: 610: 609: 606: 605: 604: 601: 597: 596:Vaught's test 594: 593: 592: 589: 588: 587: 584: 582: 579: 575: 572: 570: 567: 566: 565: 562: 560: 557: 555: 552: 550: 547: 545: 542: 540: 537: 535: 532: 528: 525: 524: 523: 520: 518: 515: 513: 510: 508: 505: 503: 500: 496: 493: 492: 491: 488: 486: 483: 479: 476: 475: 474: 471: 469: 466: 460: 457: 455: 452: 451: 450: 447: 443: 440: 438: 435: 434: 433: 430: 429: 428: 425: 421: 420:General frame 418: 417: 416: 413: 407: 404: 403: 402: 399: 398: 397: 394: 390: 387: 385: 382: 380: 377: 375: 372: 370: 367: 365: 362: 360: 357: 355: 352: 351: 350: 347: 343: 340: 339: 338: 335: 331: 328: 326: 323: 322: 321: 318: 314: 311: 309: 306: 304: 301: 300: 299: 296: 295: 291: 287: 284: 282: 279: 275: 272: 271: 270: 267: 265: 262: 260: 259:Impredicative 257: 255: 252: 250: 249: 245: 243: 240: 238: 235: 233: 230: 228: 225: 223: 220: 216: 213: 211: 208: 206: 203: 201: 198: 196: 193: 192: 191: 188: 186: 185:Formal system 183: 181: 178: 174: 171: 170: 169: 166: 164: 161: 159: 156: 152: 149: 147: 146:Non-empty set 144: 142: 139: 137: 134: 132: 129: 127: 124: 122: 119: 115: 112: 111: 110: 107: 106: 105: 102: 98: 95: 93: 90: 89: 88: 85: 81: 78: 77: 76: 73: 72: 68: 66: 64: 60: 56: 51: 49: 47: 38: 34: 33: 27: 19: 2775: 2741:Substitution 2561:Mathematical 2486:Major fields 2388:Ph.D. thesis 2379: 2372: 2334:Mizar system 2049:Strict logic 2044:Affine logic 2027:Linear logic 1944:Proof theory 1133:Polish space 1091:Analytic set 980:Aleph number 910:Zorn's lemma 732:Peano axioms 633:Stable group 559:Ultraproduct 359:Hyperinteger 292:Model theory 246: 195:Direct proof 173:Axiom schema 75:Peano axioms 52: 43: 41: 36: 31: 30: 29:Clicking on 26: 2856:WikiProject 2726:Proposition 2721:Probability 2674:Description 2615:Foundations 2339:QED project 2246:Modal logic 2200:Lambda cube 2158:Type theory 2020:Contraction 1918:Alan Turing 1903:RĂłzsa PĂ©ter 1869:NP-complete 1701:computation 1677:Mu operator 1312:∈-induction 1177:Determinacy 1003:Beth number 973:Cardinality 613:Morley rank 544:Prime model 527:Skolem hull 2881:Categories 2786:Set theory 2684:Linguistic 2679:Entailment 2669:Definition 2637:Consequent 2632:Antecedent 2415:Kurt Gödel 2367:Historical 1479:Zero sharp 1351:Set theory 1328:Well-order 987:Aleph-null 876:Set theory 638:Tame group 396:Set theory 114:Ur-element 63:algorithms 42:This is a 2817:Fallacies 2812:Paradoxes 2802:Logicians 2736:Statement 2731:Reference 2696:Induction 2659:Deduction 2622:Abduction 2592:Metalogic 2539:Classical 2503:Inference 2037:Proof net 2015:Weakening 1913:Emil Post 1667:Recursion 1662:Algorithm 1337:Power set 1228:Fuzzy set 1214:Empty set 994:Aleph-one 374:Overspill 222:Tautology 141:Empty set 136:Power set 2902:Outlines 2851:Category 2751:Validity 2652:Antinomy 2580:Theories 2544:Informal 2393:See also 2230:Finitism 2205:System F 2071:System F 767:T-schema 44:list of 2866:changes 2858: ( 2716:Premise 2647:Paradox 2477:History 2472:Outline 2361:Eurisko 1980:Sequent 2768:topics 2554:Reason 2532:Logics 2523:Syntax 2066:Ludics 1437:Subset 850:Reduct 48:topics 2795:other 2760:Lists 2746:Truth 2513:Proof 2461:Logic 2860:talk 2706:Name 2691:Form 1256:L(R) 2602:Set 2344:Coq 1184:AD+ 2883:: 2384:– 1699:, 833:/ 814:/ 65:. 50:. 2862:) 2453:e 2446:t 2439:v 1249:L 39:. 20:)

Index

Outline of mathematical logic
mathematical logic
list of topics in logic
list of computability and complexity topics
algorithms
Peano axioms
Giuseppe Peano
Mathematical induction
Structural induction
Recursive definition
Naive set theory
Element (mathematics)
Ur-element
Singleton (mathematics)
Simple theorems in the algebra of sets
Algebra of sets
Power set
Empty set
Non-empty set
Empty function
Universe (mathematics)
Axiomatization
Axiomatic system
Axiom schema
Axiomatic method
Formal system
Mathematical proof
Direct proof
Reductio ad absurdum
Proof by exhaustion

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