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Tarski himself defined truth for atomic sentences in a variant way that does not use any technical terms from semantics, such as the "expressed by" above. This is because he wanted to define these semantic terms in the context of truth. Therefore it would be circular to use one of them in the
169:
These sentences (1 and 2, etc.) have come to be called the "T-sentences". The reason they look trivial is that the object language and the metalanguage are both
English; here is an example where the object language is German and the metalanguage is English:
188:, including the problem that there is no systematic way of deciding whether a given sentence of a natural language is well-formed, and that a natural language is
672:
988:
1663:
118:). In the following, quoted text is use of the object language, while unquoted text is use of the metalanguage; a quoted sentence (such as "
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887:
224:
containing ÂŹ ("not"), ⧠("and"), âš ("or"), â ("for all"), and â ("there exists"), Tarski's inductive definition of truth looks like this:
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68:. Tarski, in "On the Concept of Truth in Formal Languages" (1935), attempted to formulate a new theory of truth in order to resolve the
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192:(that is, it can describe the semantic characteristics of its own elements). But Tarski's approach was extended by
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rendered in the object language. In this way, the metalanguage can be used to talk about the object language;
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for natural languages, which involves treating "truth" as a primitive, rather than a defined, concept. (See
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343:. A contemporary semantic definition of truth would define truth for the atomic sentences as follows:
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419:. It is a rather controversial point whether Tarski's semantic theory should be counted either as a
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definition of truth itself. Tarski's semantic conception of truth plays an important role in
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It is important to note that as Tarski originally formulated it, this theory applies only to
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72:. In the course of this he made several metamathematical discoveries, most notably
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1935) demanded that the object language be contained in the metalanguage.
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149:, holds that any viable theory of truth must entail, for every sentence "
500:
Hale, Bob; Wright, Crispin; Miller, Alexander, eds. (18 February 2017).
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instead of Tarski's logic of totally defined truth predicates) with the
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conception of truth, which is related in different ways to both the
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The
Semantic Conception of Truth and the Foundations of Semantics
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The
Semantic Conception of Truth and the Foundations of Semantics
579:
Axiomatic
Theories of Truth (Stanford Encyclopedia of Philosophy)
101:
184:. He gave a number of reasons for not extending his theory to
59:
448:
1975) is based on partial logic (a logic of partially defined
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112:) from the language that one is using to do the talking (the
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713:
304:)" is true if, and only if, for all objects x, "Fx" is true.
173:(3) 'Schnee ist weiĂ' is true if and only if snow is white.
153:", a sentence of the following form (known as "form (T)"):
126:
for a sentence, such that this name is simply the sentence
166:(2) 'snow is white' is true if and only if snow is white.
84:. Roughly, this states that a truth-predicate satisfying
733:
88:
for the sentences of a given language cannot be defined
569:
Oxford, England: Oxford
University Press, 2012, p. 110.
19:"Convention T" redirects here. Not to be confused with
567:
Quine versus
Davidson: Truth, Reference, and Meaning.
679:, Indianapolis: Hackett 1983, 2nd edition, 152â278.
38:which holds that truth is a property of sentences.
335:) can be reduced to the truth conditions of their
100:To formulate linguistic theories without semantic
2625:
499:
556:Parts of section is adapted from Kirkham, 1992.
315:)" is true if, and only if, there is an object
16:A theory of truth in the philosophy of language
673:"The Concept of Truth in Formalized Languages"
881:
749:
613:Deflationism and Semantic Theories of Truth
430:
95:
1073:
888:
874:
756:
742:
323:These explain how the truth conditions of
504:A Companion to the Philosophy of Language
728:Philosophy and Phenomenological Research
688:Philosophy and Phenomenological Research
661:, 1975. "Outline of a Theory of Truth".
209:Tarski developed the theory to give an
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895:
869:
737:
526:10.1111/b.9780631213260.1999.00015.x
714:Stanford Encyclopedia of Philosophy
705:Internet Encyclopedia of Philosophy
635:Stanford Encyclopedia of Philosophy
13:
587:
14:
2660:
694:
677:Logic, Semantics, Metamathematics
2607:
339:. The simplest constituents are
196:into an approach to theories of
122:") is always the metalanguage's
76:using the same formal technique
596:and Keith Simmons, eds., 1999.
454:strong Kleene evaluation scheme
437:Truth § Kripke's semantics
74:Tarski's undefinability theorem
58:conceptions, is due to work by
572:
559:
550:
493:
182:semantics of first-order logic
1:
2568:History of mathematical logic
486:
2493:Primitive recursive function
277:" is true if, and only if, "
258:" is true if, and only if, "
243:" is true if, and only if, "
7:
600:. Oxford University Press,
459:
371:of values to the variables
232:" is true if, and only if,
228:(1) A primitive statement "
204:truth-conditional semantics
143:material adequacy condition
10:
2665:
1557:SchröderâBernstein theorem
1284:Monadic predicate calculus
943:Foundations of mathematics
710:Tarski's Truth Definitions
631:Tarski's truth definitions
434:
367:) is true (relative to an
213:of truth as follows. (See
18:
2603:
2590:Philosophy of mathematics
2539:Automated theorem proving
2521:
2416:
2248:
2141:
1993:
1710:
1686:
1664:Von NeumannâBernaysâGödel
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1503:
1407:
1305:
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1223:
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986:
903:
802:
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481:Triune continuum paradigm
415:and also in contemporary
327:sentences (built up from
41:
701:Semantic Theory of Truth
611:Michael K Butler, 2017.
466:Disquotational principle
442:Kripke's theory of truth
431:Kripke's theory of truth
387:)) if the corresponding
132:Tarski's theory of truth
96:Tarski's theory of truth
28:semantic theory of truth
2240:Self-verifying theories
2061:Tarski's axiomatization
1012:Tarski's undefinability
1007:incompleteness theorems
319:for which "Fx" is true.
82:incompleteness theorems
2614:Mathematics portal
2225:Proof of impossibility
1873:propositional variable
1183:Propositional calculus
417:philosophy of language
36:philosophy of language
2649:Theories of deduction
2483:Kolmogorov complexity
2436:Computably enumerable
2336:Model complete theory
2128:Principia Mathematica
1188:Propositional formula
1017:BanachâTarski paradox
682:Alfred Tarski, 1944.
663:Journal of Philosophy
514:John Wiley & Sons
421:correspondence theory
2431:ChurchâTuring thesis
2418:Computability theory
1627:continuum hypothesis
1145:Square of opposition
1003:Gödel's completeness
615:. Pendlebury Press,
211:inductive definition
2585:Mathematical object
2476:P versus NP problem
2441:Computable function
2235:Reverse mathematics
2161:Logical consequence
2038:primitive recursive
2033:elementary function
1806:Free/bound variable
1659:TarskiâGrothendieck
1178:Logical connectives
1108:Logical equivalence
958:Logical consequence
425:deflationary theory
347:An atomic sentence
2634:Mathematical logic
2383:Transfer principle
2346:Semantics of logic
2331:Categorical theory
2307:Non-standard model
1821:Logical connective
948:Information theory
897:Mathematical logic
647:. Bradford Books,
471:Semantics of logic
2644:Theories of truth
2621:
2620:
2553:Abstract category
2356:Theories of truth
2166:Rule of inference
2156:Natural deduction
2137:
2136:
1682:
1681:
1387:Cartesian product
1292:
1291:
1198:Many-valued logic
1173:Boolean functions
1056:Russell's paradox
1031:diagonal argument
928:First-order logic
863:
862:
645:Theories of Truth
399:expressed by the
186:natural languages
2656:
2612:
2611:
2563:History of logic
2558:Category of sets
2451:Decision problem
2230:Ordinal analysis
2171:Sequent calculus
2069:Boolean algebras
2009:
2008:
1983:
1954:logical/constant
1708:
1707:
1694:
1617:ZermeloâFraenkel
1368:Set operations:
1303:
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1240:
1071:
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1051:LöwenheimâSkolem
938:Formal semantics
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450:truth predicates
341:atomic sentences
178:formal languages
156:(1) "P" is true
145:, also known as
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2544:Category theory
2534:Algebraic logic
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2488:Lambda calculus
2426:Church encoding
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2388:Truth predicate
2244:
2210:Complete theory
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2002:
1998:
1994:
1989:
1981:
1701: and
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1654:New Foundations
1622:axiom of choice
1605:
1567:Gödel numbering
1507: and
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1168:Boolean algebra
1154:
1118:Equiconsistency
1083:Classical logic
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1041:Halting problem
1029: and
1005: and
993: and
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987:Theorems (
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594:Simon Blackburn
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588:Further reading
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220:For a language
158:if, and only if
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665:, 72: 690â716.
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2379:
2376:
2372:
2369:
2367:
2364:
2362:
2359:
2358:
2357:
2354:
2352:
2349:
2347:
2344:
2342:
2339:
2337:
2334:
2332:
2329:
2325:
2322:
2321:
2320:
2317:
2313:
2312:of arithmetic
2310:
2309:
2308:
2305:
2301:
2298:
2296:
2293:
2291:
2288:
2286:
2283:
2281:
2278:
2277:
2276:
2273:
2269:
2266:
2264:
2261:
2260:
2259:
2256:
2255:
2253:
2251:
2247:
2241:
2238:
2236:
2233:
2231:
2228:
2226:
2223:
2220:
2219:from ZFC
2216:
2213:
2211:
2208:
2202:
2199:
2198:
2197:
2194:
2192:
2189:
2187:
2184:
2183:
2182:
2179:
2177:
2174:
2172:
2169:
2167:
2164:
2162:
2159:
2157:
2154:
2152:
2149:
2148:
2146:
2144:
2140:
2130:
2129:
2125:
2124:
2119:
2118:non-Euclidean
2116:
2112:
2109:
2107:
2104:
2102:
2101:
2097:
2096:
2094:
2091:
2090:
2088:
2084:
2080:
2077:
2075:
2072:
2071:
2070:
2066:
2062:
2059:
2058:
2057:
2053:
2049:
2046:
2044:
2041:
2039:
2036:
2034:
2031:
2029:
2026:
2024:
2021:
2020:
2018:
2014:
2013:
2011:
2006:
2000:
1995:Example
1992:
1984:
1979:
1978:
1977:
1974:
1972:
1969:
1965:
1962:
1960:
1957:
1955:
1952:
1950:
1947:
1946:
1945:
1942:
1940:
1937:
1935:
1932:
1930:
1927:
1923:
1920:
1918:
1915:
1914:
1913:
1910:
1906:
1903:
1901:
1898:
1896:
1893:
1891:
1888:
1887:
1886:
1883:
1881:
1878:
1874:
1871:
1869:
1866:
1864:
1861:
1860:
1859:
1856:
1852:
1849:
1847:
1844:
1842:
1839:
1837:
1834:
1832:
1829:
1827:
1824:
1823:
1822:
1819:
1817:
1814:
1812:
1809:
1807:
1804:
1800:
1797:
1795:
1792:
1790:
1787:
1785:
1782:
1781:
1780:
1777:
1775:
1772:
1770:
1767:
1765:
1762:
1758:
1755:
1753:
1752:by definition
1750:
1749:
1748:
1745:
1741:
1738:
1737:
1736:
1733:
1731:
1728:
1726:
1723:
1721:
1718:
1716:
1713:
1712:
1709:
1706:
1704:
1700:
1695:
1689:
1685:
1675:
1672:
1670:
1667:
1665:
1662:
1660:
1657:
1655:
1652:
1650:
1647:
1645:
1642:
1640:
1639:KripkeâPlatek
1637:
1635:
1632:
1628:
1625:
1623:
1620:
1619:
1618:
1615:
1614:
1612:
1608:
1600:
1597:
1596:
1595:
1592:
1590:
1587:
1583:
1580:
1579:
1578:
1575:
1573:
1570:
1568:
1565:
1563:
1560:
1558:
1555:
1552:
1548:
1544:
1541:
1537:
1534:
1532:
1529:
1527:
1524:
1523:
1522:
1518:
1515:
1514:
1512:
1510:
1506:
1502:
1494:
1491:
1489:
1486:
1484:
1483:constructible
1481:
1480:
1479:
1476:
1474:
1471:
1469:
1466:
1464:
1461:
1459:
1456:
1454:
1451:
1449:
1446:
1444:
1441:
1439:
1436:
1434:
1431:
1429:
1426:
1424:
1421:
1419:
1416:
1415:
1413:
1411:
1406:
1398:
1395:
1393:
1390:
1388:
1385:
1383:
1380:
1378:
1375:
1373:
1370:
1369:
1367:
1363:
1360:
1358:
1355:
1354:
1353:
1350:
1348:
1345:
1343:
1340:
1338:
1335:
1333:
1329:
1325:
1323:
1320:
1316:
1313:
1312:
1311:
1308:
1307:
1304:
1301:
1299:
1295:
1285:
1282:
1280:
1277:
1275:
1272:
1270:
1267:
1265:
1262:
1260:
1257:
1253:
1250:
1249:
1248:
1245:
1241:
1236:
1235:
1234:
1231:
1230:
1228:
1226:
1222:
1214:
1211:
1209:
1206:
1204:
1201:
1200:
1199:
1196:
1194:
1191:
1189:
1186:
1184:
1181:
1179:
1176:
1174:
1171:
1169:
1166:
1165:
1163:
1161:
1160:Propositional
1157:
1151:
1148:
1146:
1143:
1141:
1138:
1136:
1133:
1131:
1128:
1126:
1123:
1119:
1116:
1115:
1114:
1111:
1109:
1106:
1104:
1101:
1099:
1096:
1094:
1091:
1089:
1088:Logical truth
1086:
1084:
1081:
1080:
1078:
1076:
1072:
1069:
1067:
1063:
1057:
1054:
1052:
1049:
1047:
1044:
1042:
1039:
1037:
1034:
1032:
1028:
1024:
1020:
1018:
1015:
1013:
1010:
1008:
1004:
1001:
1000:
998:
996:
990:
985:
979:
976:
974:
971:
969:
966:
964:
961:
959:
956:
954:
951:
949:
946:
944:
941:
939:
936:
934:
931:
929:
926:
924:
921:
917:
914:
913:
912:
909:
908:
906:
902:
898:
891:
886:
884:
879:
877:
872:
871:
868:
856:
853:
851:
848:
846:
843:
841:
838:
836:
833:
831:
828:
826:
823:
821:
818:
816:
813:
811:
808:
807:
805:
801:
795:
792:
790:
787:
785:
782:
780:
777:
776:
774:
770:
766:
759:
754:
752:
747:
745:
740:
739:
736:
729:
725:
721:
720:Alfred Tarski
718:
715:
712:(an entry of
711:
708:
706:
702:
699:
698:
689:
685:
681:
678:
674:
670:
669:Alfred Tarski
667:
664:
660:
657:
654:
653:0-262-61108-2
650:
646:
642:
639:
636:
632:
628:
625:
622:
618:
614:
610:
607:
606:0-19-875250-4
603:
599:
595:
592:
591:
580:
575:
568:
562:
553:
537:
535:9780631213260
531:
527:
523:
519:
515:
511:
506:
505:
496:
492:
482:
479:
477:
474:
472:
469:
467:
464:
463:
457:
455:
451:
447:
443:
438:
428:
426:
422:
418:
414:
405:
402:
398:
394:
390:
385:
381:
374:
370:
365:
361:
354:
350:
346:
345:
344:
342:
338:
334:
330:
326:
318:
314:
310:
306:
303:
299:
295:
292:
288:
284:
280:
276:
272:
268:
265:
261:
257:
253:
249:
246:
242:
238:
235:
231:
227:
226:
225:
223:
218:
216:
212:
207:
205:
201:
200:
195:
191:
187:
183:
179:
174:
171:
167:
164:
163:For example,
161:
159:
154:
152:
148:
144:
139:
137:
136:Alfred Tarski
133:
129:
125:
121:
117:
116:
111:
107:
103:
93:
91:
87:
83:
79:
75:
71:
67:
66:Alfred Tarski
64:
61:
57:
53:
49:
39:
37:
33:
29:
22:
2605:
2403:Ultraproduct
2360:
2250:Model theory
2215:Independence
2151:Formal proof
2143:Proof theory
2126:
2099:
2056:real numbers
2028:second-order
1939:Substitution
1816:Metalanguage
1757:conservative
1730:Axiom schema
1674:Constructive
1644:MorseâKelley
1610:Set theories
1589:Aleph number
1582:inaccessible
1488:Grothendieck
1372:intersection
1259:Higher-order
1247:Second-order
1193:Truth tables
1150:Venn diagram
933:Formal proof
854:
830:Deflationary
789:Truth-bearer
784:Propositions
727:
704:
687:
676:
662:
644:
612:
597:
574:
566:
565:Kemp, Gary.
561:
552:
539:. Retrieved
503:
495:
441:
440:
413:modern logic
409:
403:
383:
379:
372:
363:
359:
352:
348:
337:constituents
324:
322:
316:
312:
308:
301:
297:
290:
286:
282:
278:
274:
270:
263:
259:
255:
251:
247:is not true.
244:
240:
233:
229:
221:
219:
208:
197:
189:
175:
172:
168:
165:
162:
155:
150:
147:Convention T
146:
142:
140:
131:
127:
123:
119:
115:metalanguage
113:
109:
106:liar paradox
104:such as the
99:
89:
86:Convention T
80:used in his
70:liar paradox
56:deflationary
45:
27:
25:
2513:Type theory
2461:undecidable
2393:Truth value
2280:equivalence
1959:non-logical
1572:Enumeration
1562:Isomorphism
1509:cardinality
1493:Von Neumann
1458:Ultrafilter
1423:Uncountable
1357:equivalence
1274:Quantifiers
1264:Fixed-point
1233:First-order
1113:Consistency
1098:Proposition
1075:Traditional
1046:Lindström's
1036:Compactness
978:Type theory
923:Cardinality
794:Truth-maker
659:Saul Kripke
541:28 February
516:. pp.
512:, England:
510:West Sussex
446:Saul Kripke
333:quantifiers
329:connectives
180:, cf. also
2628:Categories
2324:elementary
2017:arithmetic
1885:Quantifier
1863:functional
1735:Expression
1453:Transitive
1397:identities
1382:complement
1315:hereditary
1298:Set theory
850:Redundancy
621:0993594549
487:References
435:See also:
369:assignment
291:B" is true
287:A" is true
283:B" is true
279:A" is true
264:B" is true
260:A" is true
78:Kurt Gödel
2639:Semantics
2595:Supertask
2498:Recursion
2456:decidable
2290:saturated
2268:of models
2191:deductive
2186:axiomatic
2106:Hilbert's
2093:Euclidean
2074:canonical
1997:axiomatic
1929:Signature
1858:Predicate
1747:Extension
1669:Ackermann
1594:Operation
1473:Universal
1463:Recursive
1438:Singleton
1433:Inhabited
1418:Countable
1408:Types of
1392:power set
1362:partition
1279:Predicate
1225:Predicate
1140:Syllogism
1130:Soundness
1103:Inference
1093:Tautology
995:paradoxes
845:Pragmatic
840:Pluralist
835:Epistemic
815:Consensus
810:Coherence
779:Statement
722:, 1944.
633:. In the
401:predicate
395:bear the
393:variables
141:Tarski's
102:paradoxes
2580:Logicism
2573:timeline
2549:Concrete
2408:Validity
2378:T-schema
2371:Kripke's
2366:Tarski's
2361:semantic
2351:Strength
2300:submodel
2295:spectrum
2263:function
2111:Tarski's
2100:Elements
2087:geometry
2043:Robinson
1964:variable
1949:function
1922:spectrum
1912:Sentence
1868:variable
1811:Language
1764:Relation
1725:Automata
1715:Alphabet
1699:language
1553:-jection
1531:codomain
1517:Function
1478:Universe
1448:Infinite
1352:Relation
1135:Validity
1125:Argument
1023:theorem,
855:Semantic
803:Theories
671:, 1935.
643:, 1992.
629:, 2001.
547:, p. 326
476:T-schema
460:See also
423:or as a
397:relation
215:T-schema
194:Davidson
63:logician
48:semantic
21:T-schema
2522:Related
2319:Diagram
2217: (
2196:Hilbert
2181:Systems
2176:Theorem
2054:of the
1999:systems
1779:Formula
1774:Grammar
1690: (
1634:General
1347:Forcing
1332:Element
1252:Monadic
1027:paradox
968:Theorem
904:General
772:General
378:, ...,
325:complex
199:meaning
34:in the
2285:finite
2048:Skolem
2001:
1976:Theory
1944:Symbol
1934:String
1917:atomic
1794:ground
1789:closed
1784:atomic
1740:ground
1703:syntax
1599:binary
1526:domain
1443:Finite
1208:finite
1066:Logics
1025:
973:Theory
651:
619:
604:
532:
520:â330.
389:values
307:(6) "â
296:(5) "â
239:(2) "ÂŹ
190:closed
90:within
60:Polish
42:Origin
2275:Model
2023:Peano
1880:Proof
1720:Arity
1649:Naive
1536:image
1468:Fuzzy
1428:Empty
1377:union
1322:Class
963:Model
953:Lemma
911:Axiom
765:Truth
598:Truth
358:,...,
289:and "
285:or ("
269:(4) "
262:and "
250:(3) "
160:, P.
30:is a
2398:Type
2201:list
2005:list
1982:list
1971:Term
1905:rank
1799:open
1693:list
1505:Maps
1410:sets
1269:Free
1239:list
989:list
916:list
649:ISBN
617:ISBN
602:ISBN
543:2024
530:ISBN
331:and
281:or "
124:name
54:and
46:The
2085:of
2067:of
2015:of
1547:Sur
1521:Map
1328:Ur-
1310:Set
726:.
522:doi
518:309
391:of
206:.)
2630::
2471:NP
2095::
2089::
2019::
1696:),
1551:Bi
1543:In
730:4.
703:,
690:4.
686:.
675:.
528:.
508:.
456:.
427:.
313:Fx
302:Fx
293:).
245:A"
217:)
26:A
2551:/
2466:P
2221:)
2007:)
2003:(
1900:â
1895:!
1890:â
1851:=
1846:â
1841:â
1836:â§
1831:âš
1826:ÂŹ
1549:/
1545:/
1519:/
1330:)
1326:(
1213:â
1203:3
991:)
889:e
882:t
875:v
757:e
750:t
743:v
716:)
655:.
637:.
623:.
608:.
545:.
524::
444:(
406:.
404:F
384:n
380:x
376:1
373:x
364:n
360:x
356:1
353:x
351:(
349:F
317:x
311:(
309:x
300:(
298:x
275:B
273:âš
271:A
266:.
256:B
254:â§
252:A
241:A
236:.
234:A
230:A
222:L
151:P
134:(
128:P
120:P
23:.
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