2426:
2496:
565:
A is a computable set if and only if it is either the range of a nondecreasing total computable function, or the empty set. The image of a computable set under a nondecreasing total computable function is computable.
384:
The set of Gödel numbers of arithmetic proofs described in Kurt Gödel's paper "On formally undecidable propositions of
Principia Mathematica and related systems I" is computable; see
58:
which takes a number as input, terminates after a finite amount of time (possibly depending on the given number) and correctly decides whether the number belongs to the set or not.
322:
556:
266:
240:
205:
179:
358:
286:
144:
110:
805:
664:
2953:
1480:
1563:
704:
1877:
2035:
523:
is computable. (In general, the image of a computable set under a computable function is c.e., but possibly not computable).
823:
385:
2642:
2462:
1890:
1213:
2970:
1895:
1885:
1622:
1475:
828:
819:
2031:
650:
636:
628:
614:
606:
1373:
2128:
1872:
697:
2948:
1433:
1126:
575:
2828:
867:
3108:
2389:
2091:
1854:
1849:
1674:
1095:
779:
3103:
2722:
2601:
2384:
2167:
2084:
1797:
1728:
1605:
847:
17:
2965:
2309:
2135:
1821:
1455:
1054:
396:
80:
sets. For these sets, it is only required that there is an algorithm that correctly decides when a number
2958:
2596:
2559:
2187:
2182:
1792:
1531:
1460:
789:
690:
2116:
1706:
1100:
1068:
759:
423:
2613:
298:
2647:
2539:
2527:
2522:
2406:
2355:
2252:
1750:
1711:
1188:
833:
529:
862:
361:) is computable; that is, the set of natural numbers less than a given natural number is computable.
84:
in the set; the algorithm may give no answer (but not the wrong answer) for numbers not in the set.
2455:
2247:
2177:
1716:
1568:
1551:
1274:
754:
3067:
2985:
2860:
2812:
2626:
2549:
2079:
2056:
2017:
1903:
1844:
1490:
1410:
1254:
1198:
811:
497:
480:
440:
3019:
2900:
2712:
2532:
2369:
2096:
2074:
2041:
1934:
1780:
1765:
1738:
1689:
1573:
1508:
1333:
1299:
1294:
1168:
999:
976:
559:
245:
2935:
2905:
2849:
2769:
2749:
2727:
2299:
2152:
1944:
1662:
1398:
1304:
1163:
1148:
1029:
1004:
505:
73:
210:
184:
149:
3009:
2999:
2833:
2764:
2717:
2657:
2544:
2272:
2234:
2111:
1915:
1755:
1679:
1657:
1485:
1443:
1342:
1309:
1173:
961:
872:
417:
31:
8:
3004:
2915:
2823:
2818:
2632:
2574:
2512:
2448:
2401:
2292:
2277:
2257:
2214:
2101:
2051:
1977:
1922:
1859:
1652:
1647:
1595:
1363:
1352:
1024:
924:
852:
843:
839:
774:
769:
516:
325:
124:
2927:
2922:
2707:
2662:
2569:
2430:
2199:
2162:
2147:
2140:
2123:
1927:
1909:
1775:
1701:
1684:
1637:
1450:
1359:
1193:
1178:
1138:
1090:
1075:
1063:
1019:
994:
764:
713:
580:
374:
293:
271:
129:
95:
1383:
2784:
2621:
2584:
2554:
2485:
2425:
2365:
2172:
1982:
1972:
1864:
1745:
1580:
1556:
1337:
1321:
1226:
1203:
1080:
1049:
1014:
909:
744:
646:
632:
624:
610:
602:
410:
35:
3072:
3062:
3047:
3042:
2910:
2564:
2379:
2374:
2267:
2224:
2046:
2007:
2002:
1987:
1813:
1770:
1667:
1465:
1415:
989:
951:
668:
2941:
2879:
2697:
2517:
2360:
2350:
2304:
2287:
2242:
2204:
2106:
2026:
1833:
1760:
1733:
1721:
1627:
1541:
1515:
1470:
1438:
1239:
1041:
984:
934:
899:
857:
403:
378:
344:
subset of the natural numbers is computable. This includes these special cases:
3077:
2874:
2759:
2744:
2701:
2637:
2579:
2345:
2324:
2282:
2157:
2012:
1610:
1600:
1590:
1585:
1519:
1393:
1269:
1158:
1153:
1131:
732:
513:
490:
289:
121:
113:
39:
3097:
3082:
2884:
2798:
2793:
2319:
1997:
1504:
1289:
1279:
1249:
1234:
904:
3052:
519:
is a computable set. The image of a computable set under a total computable
3032:
3027:
2845:
2774:
2732:
2591:
2495:
2219:
2066:
1967:
1959:
1839:
1787:
1696:
1632:
1615:
1546:
1405:
1264:
966:
749:
367:
3057:
2692:
2329:
2209:
1388:
1378:
1325:
1009:
929:
914:
794:
739:
3037:
2808:
2471:
1259:
1114:
1085:
891:
72:
A more general class of sets than the computable ones consists of the
2840:
2803:
2754:
2652:
2411:
2314:
1367:
1284:
1244:
1208:
1144:
956:
946:
919:
682:
673:
585:
520:
348:
55:
645:
Perspectives in
Mathematical Logic. Springer-Verlag, Berlin, 1987.
2396:
2194:
1642:
1347:
941:
509:
341:
1992:
784:
2865:
2687:
2737:
2504:
2440:
1536:
882:
727:
621:
The Theory of
Recursive Functions and Effective Computability
662:
601:
Cambridge
University Press, Cambridge-New York, 1980.
532:
413:
of two finite simplicial complexes is not computable.
301:
274:
248:
213:
187:
152:
132:
98:
526:
A is a computable set if and only if it is at level
550:
316:
280:
260:
234:
199:
173:
138:
104:
3095:
354:The entire set of natural numbers is computable.
2456:
698:
331:
2463:
2449:
890:
705:
691:
304:
643:Recursively enumerable sets and degrees.
61:A set which is not computable is called
14:
3096:
712:
2444:
686:
663:
87:
24:
534:
25:
3120:
656:
359:as defined in standard set theory
74:computably enumerable (c.e.) sets
2494:
2424:
317:{\displaystyle \mathbb {1} _{S}}
576:Recursively enumerable language
551:{\displaystyle \Delta _{1}^{0}}
386:Gödel's incompleteness theorems
27:Concept in computability theory
2470:
223:
217:
162:
156:
13:
1:
2385:History of mathematical logic
591:
439:is a computable set then the
430:
2310:Primitive recursive function
512:of a computable set under a
397:List of undecidable problems
377:is a computable subset of a
7:
569:
10:
3125:
2954:von NeumannâBernaysâGödel
1374:SchröderâBernstein theorem
1101:Monadic predicate calculus
760:Foundations of mathematics
394:
268:. In other words, the set
3018:
2981:
2893:
2783:
2755:One-to-one correspondence
2671:
2612:
2503:
2492:
2478:
2420:
2407:Philosophy of mathematics
2356:Automated theorem proving
2338:
2233:
2065:
1958:
1810:
1527:
1503:
1481:Von NeumannâBernaysâGödel
1426:
1320:
1224:
1122:
1113:
1040:
975:
881:
803:
720:
455:are computable sets then
404:Turing machines that halt
332:Examples and non-examples
261:{\displaystyle x\notin S}
447:is a computable set. If
2057:Self-verifying theories
1878:Tarski's axiomatization
829:Tarski's undefinability
824:incompleteness theorems
481:Cantor pairing function
424:Hilbert's tenth problem
2713:Constructible universe
2540:Constructibility (V=L)
2431:Mathematics portal
2042:Proof of impossibility
1690:propositional variable
1000:Propositional calculus
560:arithmetical hierarchy
552:
318:
282:
262:
236:
235:{\displaystyle f(x)=0}
201:
200:{\displaystyle x\in S}
175:
174:{\displaystyle f(x)=1}
140:
106:
3109:Theory of computation
2936:Principia Mathematica
2770:Transfinite induction
2629:(i.e. set difference)
2300:Kolmogorov complexity
2253:Computably enumerable
2153:Model complete theory
1945:Principia Mathematica
1005:Propositional formula
834:BanachâTarski paradox
553:
506:computably enumerable
483:are computable sets.
418:busy beaver champions
357:Each natural number (
319:
283:
263:
237:
202:
176:
141:
107:
3104:Computability theory
3010:Burali-Forti paradox
2765:Set-builder notation
2718:Continuum hypothesis
2658:Symmetric difference
2248:ChurchâTuring thesis
2235:Computability theory
1444:continuum hypothesis
962:Square of opposition
820:Gödel's completeness
530:
489:is a computable set
299:
272:
246:
211:
185:
150:
130:
96:
32:computability theory
2971:TarskiâGrothendieck
2402:Mathematical object
2293:P versus NP problem
2258:Computable function
2052:Reverse mathematics
1978:Logical consequence
1855:primitive recursive
1850:elementary function
1623:Free/bound variable
1476:TarskiâGrothendieck
995:Logical connectives
925:Logical equivalence
775:Logical consequence
547:
517:computable function
125:computable function
2560:Limitation of size
2200:Transfer principle
2163:Semantics of logic
2148:Categorical theory
2124:Non-standard model
1638:Logical connective
765:Information theory
714:Mathematical logic
581:Recursive language
548:
533:
426:is not computable.
420:is not computable.
406:is not computable.
375:recursive language
314:
294:indicator function
278:
258:
232:
197:
171:
136:
120:if there exists a
102:
3091:
3090:
3000:Russell's paradox
2949:ZermeloâFraenkel
2850:Dedekind-infinite
2723:Diagonal argument
2622:Cartesian product
2486:Set (mathematics)
2438:
2437:
2370:Abstract category
2173:Theories of truth
1983:Rule of inference
1973:Natural deduction
1954:
1953:
1499:
1498:
1204:Cartesian product
1109:
1108:
1015:Many-valued logic
990:Boolean functions
873:Russell's paradox
848:diagonal argument
745:First-order logic
471:and the image of
411:isomorphism class
281:{\displaystyle S}
139:{\displaystyle f}
105:{\displaystyle S}
88:Formal definition
16:(Redirected from
3116:
3073:Bertrand Russell
3063:John von Neumann
3048:Abraham Fraenkel
3043:Richard Dedekind
3005:Suslin's problem
2916:Cantor's theorem
2633:De Morgan's laws
2498:
2465:
2458:
2451:
2442:
2441:
2429:
2428:
2380:History of logic
2375:Category of sets
2268:Decision problem
2047:Ordinal analysis
1988:Sequent calculus
1886:Boolean algebras
1826:
1825:
1800:
1771:logical/constant
1525:
1524:
1511:
1434:ZermeloâFraenkel
1185:Set operations:
1120:
1119:
1057:
888:
887:
868:LöwenheimâSkolem
755:Formal semantics
707:
700:
693:
684:
683:
679:
678:
557:
555:
554:
549:
546:
541:
340:Every finite or
323:
321:
320:
315:
313:
312:
307:
287:
285:
284:
279:
267:
265:
264:
259:
241:
239:
238:
233:
206:
204:
203:
198:
180:
178:
177:
172:
145:
143:
142:
137:
111:
109:
108:
103:
21:
3124:
3123:
3119:
3118:
3117:
3115:
3114:
3113:
3094:
3093:
3092:
3087:
3014:
2993:
2977:
2942:New Foundations
2889:
2779:
2698:Cardinal number
2681:
2667:
2608:
2499:
2490:
2474:
2469:
2439:
2434:
2423:
2416:
2361:Category theory
2351:Algebraic logic
2334:
2305:Lambda calculus
2243:Church encoding
2229:
2205:Truth predicate
2061:
2027:Complete theory
1950:
1819:
1815:
1811:
1806:
1798:
1518: and
1514:
1509:
1495:
1471:New Foundations
1439:axiom of choice
1422:
1384:Gödel numbering
1324: and
1316:
1220:
1105:
1055:
1036:
985:Boolean algebra
971:
935:Equiconsistency
900:Classical logic
877:
858:Halting problem
846: and
822: and
810: and
809:
804:Theorems (
799:
716:
711:
669:"Recursive Set"
659:
594:
572:
542:
537:
531:
528:
527:
433:
399:
379:formal language
334:
308:
303:
302:
300:
297:
296:
273:
270:
269:
247:
244:
243:
212:
209:
208:
186:
183:
182:
151:
148:
147:
131:
128:
127:
114:natural numbers
97:
94:
93:
90:
54:if there is an
40:natural numbers
28:
23:
22:
15:
12:
11:
5:
3122:
3112:
3111:
3106:
3089:
3088:
3086:
3085:
3080:
3078:Thoralf Skolem
3075:
3070:
3065:
3060:
3055:
3050:
3045:
3040:
3035:
3030:
3024:
3022:
3016:
3015:
3013:
3012:
3007:
3002:
2996:
2994:
2992:
2991:
2988:
2982:
2979:
2978:
2976:
2975:
2974:
2973:
2968:
2963:
2962:
2961:
2946:
2945:
2944:
2932:
2931:
2930:
2919:
2918:
2913:
2908:
2903:
2897:
2895:
2891:
2890:
2888:
2887:
2882:
2877:
2872:
2863:
2858:
2853:
2843:
2838:
2837:
2836:
2831:
2826:
2816:
2806:
2801:
2796:
2790:
2788:
2781:
2780:
2778:
2777:
2772:
2767:
2762:
2760:Ordinal number
2757:
2752:
2747:
2742:
2741:
2740:
2735:
2725:
2720:
2715:
2710:
2705:
2695:
2690:
2684:
2682:
2680:
2679:
2676:
2672:
2669:
2668:
2666:
2665:
2660:
2655:
2650:
2645:
2640:
2638:Disjoint union
2635:
2630:
2624:
2618:
2616:
2610:
2609:
2607:
2606:
2605:
2604:
2599:
2588:
2587:
2585:Martin's axiom
2582:
2577:
2572:
2567:
2562:
2557:
2552:
2550:Extensionality
2547:
2542:
2537:
2536:
2535:
2530:
2525:
2515:
2509:
2507:
2501:
2500:
2493:
2491:
2489:
2488:
2482:
2480:
2476:
2475:
2468:
2467:
2460:
2453:
2445:
2436:
2435:
2421:
2418:
2417:
2415:
2414:
2409:
2404:
2399:
2394:
2393:
2392:
2382:
2377:
2372:
2363:
2358:
2353:
2348:
2346:Abstract logic
2342:
2340:
2336:
2335:
2333:
2332:
2327:
2325:Turing machine
2322:
2317:
2312:
2307:
2302:
2297:
2296:
2295:
2290:
2285:
2280:
2275:
2265:
2263:Computable set
2260:
2255:
2250:
2245:
2239:
2237:
2231:
2230:
2228:
2227:
2222:
2217:
2212:
2207:
2202:
2197:
2192:
2191:
2190:
2185:
2180:
2170:
2165:
2160:
2158:Satisfiability
2155:
2150:
2145:
2144:
2143:
2133:
2132:
2131:
2121:
2120:
2119:
2114:
2109:
2104:
2099:
2089:
2088:
2087:
2082:
2075:Interpretation
2071:
2069:
2063:
2062:
2060:
2059:
2054:
2049:
2044:
2039:
2029:
2024:
2023:
2022:
2021:
2020:
2010:
2005:
1995:
1990:
1985:
1980:
1975:
1970:
1964:
1962:
1956:
1955:
1952:
1951:
1949:
1948:
1940:
1939:
1938:
1937:
1932:
1931:
1930:
1925:
1920:
1900:
1899:
1898:
1896:minimal axioms
1893:
1882:
1881:
1880:
1869:
1868:
1867:
1862:
1857:
1852:
1847:
1842:
1829:
1827:
1808:
1807:
1805:
1804:
1803:
1802:
1790:
1785:
1784:
1783:
1778:
1773:
1768:
1758:
1753:
1748:
1743:
1742:
1741:
1736:
1726:
1725:
1724:
1719:
1714:
1709:
1699:
1694:
1693:
1692:
1687:
1682:
1672:
1671:
1670:
1665:
1660:
1655:
1650:
1645:
1635:
1630:
1625:
1620:
1619:
1618:
1613:
1608:
1603:
1593:
1588:
1586:Formation rule
1583:
1578:
1577:
1576:
1571:
1561:
1560:
1559:
1549:
1544:
1539:
1534:
1528:
1522:
1505:Formal systems
1501:
1500:
1497:
1496:
1494:
1493:
1488:
1483:
1478:
1473:
1468:
1463:
1458:
1453:
1448:
1447:
1446:
1441:
1430:
1428:
1424:
1423:
1421:
1420:
1419:
1418:
1408:
1403:
1402:
1401:
1394:Large cardinal
1391:
1386:
1381:
1376:
1371:
1357:
1356:
1355:
1350:
1345:
1330:
1328:
1318:
1317:
1315:
1314:
1313:
1312:
1307:
1302:
1292:
1287:
1282:
1277:
1272:
1267:
1262:
1257:
1252:
1247:
1242:
1237:
1231:
1229:
1222:
1221:
1219:
1218:
1217:
1216:
1211:
1206:
1201:
1196:
1191:
1183:
1182:
1181:
1176:
1166:
1161:
1159:Extensionality
1156:
1154:Ordinal number
1151:
1141:
1136:
1135:
1134:
1123:
1117:
1111:
1110:
1107:
1106:
1104:
1103:
1098:
1093:
1088:
1083:
1078:
1073:
1072:
1071:
1061:
1060:
1059:
1046:
1044:
1038:
1037:
1035:
1034:
1033:
1032:
1027:
1022:
1012:
1007:
1002:
997:
992:
987:
981:
979:
973:
972:
970:
969:
964:
959:
954:
949:
944:
939:
938:
937:
927:
922:
917:
912:
907:
902:
896:
894:
885:
879:
878:
876:
875:
870:
865:
860:
855:
850:
838:Cantor's
836:
831:
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665:Sakharov, Alex
658:
657:External links
655:
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599:Computability.
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491:if and only if
432:
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395:Main article:
392:Non-examples:
390:
389:
382:
371:
370:is computable.
366:The subset of
364:
363:
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355:
352:
351:is computable.
333:
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290:if and only if
288:is computable
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76:, also called
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3:
2:
3121:
3110:
3107:
3105:
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3101:
3099:
3084:
3083:Ernst Zermelo
3081:
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3068:Willard Quine
3066:
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3044:
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3039:
3036:
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3026:
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3023:
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3020:Set theorists
3017:
3011:
3008:
3006:
3003:
3001:
2998:
2997:
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2966:KripkeâPlatek
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2602:specification
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2320:Recursive set
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2139:
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2134:
2130:
2129:of arithmetic
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2068:
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2043:
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2037:
2036:from ZFC
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2019:
2016:
2015:
2014:
2011:
2009:
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2001:
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1935:non-Euclidean
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1924:
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1812:Example
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1569:by definition
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1456:KripkeâPlatek
1454:
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1319:
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1301:
1300:constructible
1298:
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1099:
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1021:
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1016:
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1006:
1003:
1001:
998:
996:
993:
991:
988:
986:
983:
982:
980:
978:
977:Propositional
974:
968:
965:
963:
960:
958:
955:
953:
950:
948:
945:
943:
940:
936:
933:
932:
931:
928:
926:
923:
921:
918:
916:
913:
911:
908:
906:
905:Logical truth
903:
901:
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895:
893:
889:
886:
884:
880:
874:
871:
869:
866:
864:
861:
859:
856:
854:
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841:
837:
835:
832:
830:
827:
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821:
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815:
813:
807:
802:
796:
793:
791:
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783:
781:
778:
776:
773:
771:
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766:
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761:
758:
756:
753:
751:
748:
746:
743:
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734:
731:
730:
729:
726:
725:
723:
719:
715:
708:
703:
701:
696:
694:
689:
688:
685:
676:
675:
670:
666:
661:
660:
652:
651:3-540-15299-7
648:
644:
640:
638:
637:0-07-053522-1
634:
630:
629:0-262-68052-1
626:
623:, MIT Press.
622:
619:Rogers, H.
618:
616:
615:0-521-29465-7
612:
608:
607:0-521-22384-9
604:
600:
596:
595:
587:
584:
582:
579:
577:
574:
573:
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543:
538:
524:
522:
518:
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511:
507:
503:
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492:
488:
484:
482:
478:
474:
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450:
446:
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438:
425:
422:
419:
415:
412:
408:
405:
401:
400:
398:
393:
387:
383:
380:
376:
372:
369:
368:prime numbers
365:
360:
356:
353:
350:
346:
345:
343:
339:
338:
337:
329:
327:
309:
295:
291:
275:
255:
252:
249:
229:
226:
220:
214:
194:
191:
188:
168:
165:
159:
153:
133:
126:
123:
119:
115:
99:
85:
83:
79:
78:semidecidable
75:
70:
68:
64:
63:noncomputable
59:
57:
53:
49:
45:
41:
37:
33:
19:
18:Recursive set
3033:Georg Cantor
3028:Paul Bernays
2959:MorseâKelley
2934:
2867:
2866:Subset
2855:
2813:hereditarily
2775:Venn diagram
2733:ordered pair
2648:Intersection
2592:Axiom schema
2422:
2262:
2220:Ultraproduct
2067:Model theory
2032:Independence
1968:Formal proof
1960:Proof theory
1943:
1916:
1873:real numbers
1845:second-order
1756:Substitution
1633:Metalanguage
1574:conservative
1547:Axiom schema
1491:Constructive
1461:MorseâKelley
1427:Set theories
1406:Aleph number
1399:inaccessible
1305:Grothendieck
1189:intersection
1076:Higher-order
1064:Second-order
1010:Truth tables
967:Venn diagram
750:Formal proof
672:
642:
620:
598:
597:Cutland, N.
564:
525:
508:(c.e.). The
501:
493:
486:
485:
476:
472:
468:
464:
460:
456:
452:
448:
444:
436:
434:
391:
335:
117:
91:
81:
77:
71:
66:
62:
60:
51:
47:
43:
29:
3058:Thomas Jech
2901:Alternative
2880:Uncountable
2834:Ultrafilter
2693:Cardinality
2597:replacement
2545:Determinacy
2330:Type theory
2278:undecidable
2210:Truth value
2097:equivalence
1776:non-logical
1389:Enumeration
1379:Isomorphism
1326:cardinality
1310:Von Neumann
1275:Ultrafilter
1240:Uncountable
1174:equivalence
1091:Quantifiers
1081:Fixed-point
1050:First-order
930:Consistency
915:Proposition
892:Traditional
863:Lindström's
853:Compactness
795:Type theory
740:Cardinality
416:The set of
402:The set of
67:undecidable
3098:Categories
3053:Kurt Gödel
3038:Paul Cohen
2875:Transitive
2643:Identities
2627:Complement
2614:Operations
2575:Regularity
2513:Adjunction
2472:Set theory
2141:elementary
1834:arithmetic
1702:Quantifier
1680:functional
1552:Expression
1270:Transitive
1214:identities
1199:complement
1132:hereditary
1115:Set theory
641:Soare, R.
592:References
498:complement
479:under the
441:complement
431:Properties
336:Examples:
326:computable
146:such that
118:computable
116:is called
44:computable
42:is called
2986:Paradoxes
2906:Axiomatic
2885:Universal
2861:Singleton
2856:Recursive
2799:Countable
2794:Amorphous
2653:Power set
2570:Power set
2528:dependent
2523:countable
2412:Supertask
2315:Recursion
2273:decidable
2107:saturated
2085:of models
2008:deductive
2003:axiomatic
1923:Hilbert's
1910:Euclidean
1891:canonical
1814:axiomatic
1746:Signature
1675:Predicate
1564:Extension
1486:Ackermann
1411:Operation
1290:Universal
1280:Recursive
1255:Singleton
1250:Inhabited
1235:Countable
1225:Types of
1209:power set
1179:partition
1096:Predicate
1042:Predicate
957:Syllogism
947:Soundness
920:Inference
910:Tautology
812:paradoxes
674:MathWorld
586:Recursion
535:Δ
521:bijection
504:are both
349:empty set
253:∉
192:∈
92:A subset
56:algorithm
52:decidable
48:recursive
2990:Problems
2894:Theories
2870:Superset
2846:Infinite
2675:Concepts
2555:Infinity
2479:Overview
2397:Logicism
2390:timeline
2366:Concrete
2225:Validity
2195:T-schema
2188:Kripke's
2183:Tarski's
2178:semantic
2168:Strength
2117:submodel
2112:spectrum
2080:function
1928:Tarski's
1917:Elements
1904:geometry
1860:Robinson
1781:variable
1766:function
1739:spectrum
1729:Sentence
1685:variable
1628:Language
1581:Relation
1542:Automata
1532:Alphabet
1516:language
1370:-jection
1348:codomain
1334:Function
1295:Universe
1265:Infinite
1169:Relation
952:Validity
942:Argument
840:theorem,
570:See also
510:preimage
496:and the
342:cofinite
2928:General
2923:Zermelo
2829:subbase
2811: (
2750:Forcing
2728:Element
2700: (
2678:Methods
2565:Pairing
2339:Related
2136:Diagram
2034: (
2013:Hilbert
1998:Systems
1993:Theorem
1871:of the
1816:systems
1596:Formula
1591:Grammar
1507: (
1451:General
1164:Forcing
1149:Element
1069:Monadic
844:paradox
785:Theorem
721:General
558:of the
112:of the
2819:Filter
2809:Finite
2745:Family
2688:Almost
2533:global
2518:Choice
2505:Axioms
2102:finite
1865:Skolem
1818:
1793:Theory
1761:Symbol
1751:String
1734:atomic
1611:ground
1606:closed
1601:atomic
1557:ground
1520:syntax
1416:binary
1343:domain
1260:Finite
1025:finite
883:Logics
842:
790:Theory
649:
635:
627:
613:
605:
2911:Naive
2841:Fuzzy
2804:Empty
2787:types
2738:tuple
2708:Class
2702:large
2663:Union
2580:Union
2092:Model
1840:Peano
1697:Proof
1537:Arity
1466:Naive
1353:image
1285:Fuzzy
1245:Empty
1194:union
1139:Class
780:Model
770:Lemma
728:Axiom
514:total
122:total
50:, or
2824:base
2215:Type
2018:list
1822:list
1799:list
1788:Term
1722:rank
1616:open
1510:list
1322:Maps
1227:sets
1086:Free
1056:list
806:list
733:list
647:ISBN
633:ISBN
625:ISBN
611:ISBN
603:ISBN
451:and
409:The
347:The
292:the
207:and
34:, a
2785:Set
1902:of
1884:of
1832:of
1364:Sur
1338:Map
1145:Ur-
1127:Set
631:;
500:of
443:of
435:If
324:is
242:if
181:if
65:or
38:of
36:set
30:In
3100::
2288:NP
1912::
1906::
1836::
1513:),
1368:Bi
1360:In
671:.
667:.
609:;
562:.
475:Ă
467:âȘ
463:,
459:â©
373:A
328:.
82:is
69:.
46:,
2868:·
2852:)
2848:(
2815:)
2704:)
2464:e
2457:t
2450:v
2368:/
2283:P
2038:)
1824:)
1820:(
1717:â
1712:!
1707:â
1668:=
1663:â
1658:â
1653:â§
1648:âš
1643:ÂŹ
1366:/
1362:/
1336:/
1147:)
1143:(
1030:â
1020:3
808:)
706:e
699:t
692:v
677:.
544:0
539:1
502:A
494:A
487:A
477:B
473:A
469:B
465:A
461:B
457:A
453:B
449:A
445:A
437:A
388:.
381:.
310:S
305:1
276:S
256:S
250:x
230:0
227:=
224:)
221:x
218:(
215:f
195:S
189:x
169:1
166:=
163:)
160:x
157:(
154:f
134:f
100:S
20:)
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