ACKERMANN, WILHELM (also see Hilbert and —)
1924-5.Begrundung des "tertium non datur" mittels der Hilbertschen Theorie der Widerspruchsfreiheit. Mathematische Annalen, vol. 93, pp. 1-36.
1940. Zur Widerspruchsfreiheit der Zahlentheorie. Ibid., vol. 117, pp. 162-194.
ADDISON, J. W.
1960. The theory of hierarchies. Logic, methodology and philosophy of science: Proceedings of the 1960 International Congress (Stanford, Aug. 24-Sept. 2), ed. by Nagel, Suppes and Tarski, Stanford, Calif. (Stanford Univ. Press) 1962, pp. 26-37.
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1965. (editors) The theory of models, Proceedings of 1963 the International Symposium at Berkeley. Amsterdam (North-Holland Pub. Co.), XV+494 pp.
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1892. Mathematical recreations and essays. 1st. ed. 1892; 11th. ed., revised by H. S. M. Coxeter, New York (Macmillan) 1939, xvi+418 pp.
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1961. On formal properties of simple phase structure grammars. Zeitschrift fur Phonetik, Sprachwissenschaft und Kommunikationsforschung, vol. 14, pp. 143-172.
BENACERRAF, PAUL and PUTNAM, HILARY
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BERNAYS, PAUL (also — and FRAENKEL; HILBERT and —)
1937-1954. A system of axiomatic set theory—Parts I-VIL The journal of symbolic logic, vol. 2 (1937), pp. 65-77, vol. 6 (1941), pp. 1-17, vol. 7 (1942), pp. 65-89, 133-145, vol. 8 (1943), pp. 89-106, vol. 13 (1948), pp. 65-79, vol. 19 (1954), pp. 81-96.
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1958. Axiomatic set theory, by Bernays, with a historical introduction by Fraenkel (pp. 3-35). Amsterdam (North-Holland Pub. Co.), VIII+226 pp.
BERNSTEIN, ALLEN R. and ROBINSON, ABRAHAM
1966 (abstract 1964). Solution of an invariant subspace problem of K. T. Smith and P. R. Halmos. Pacific journal of mathematics, vol. 16, pp. 421-431. Abstract in Notices of the American Mathematical Society, vol. 11, p. 586.
1951.A topological proof of the theorem of Lowenheim-Skolem-Godel. Koninklijke
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1955. Semantic entailment and formal derivability. Mededelingen der Koninklijke Nederlandse Akademie van Wetenschappen (Amsterdam), Afd. letterkunde, n.s., vol. 18, no. 13, pp. 309-342.
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1958. An analysis of Turing's "The word problem in semi-groups with cancellation". Annals of mathematics, 2 s., vol. 67, pp. 195-202.
1959. The word problem. Ibid., vol. 70, pp. 207-265.
1966. Word problems and recursively enumerable degrees of unsolvability. A first paper on Thue systems. Ibid., vol. 83, pp. 520-571.
1966a. Word problems and recursively enumerable degrees of unsolvability. A sequel on finitely presented groups. Ibid., vol. 84, pp. 49-84.
1967. Decision problems about algebraic and logical systems as a whole and recursively enumerable degrees of unsolvability. To appear in the proceedings of the 1966 "Kolloquium uber Logik und Grundlagen der Mathematik" in Hannover.
BOONE, W. W., HAKEN, WOLFGANG and POENARU, VALENTIN
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BOREL, EMILE
1898. Lecons sur la theorie des fonctions. Paris, 8 + 136 pp. 4th ed. (Lecons sur la theorie des fonctions; principes de la theorie des ensembles en vue des applications a la theorie des fonctions), Paris (Gauthier-Villars) 1950, xii+295 pp.
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1958. The word problem for groups. Proceedings of the London Mathematical Society, 3 s., vol. 8 (1958), pp. 493-506.
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1935. Ein Gultigkeitskriterium fur die Satze der klassischen Mathematik. Monat-shefte fur Mathematik und Physik, vol. 42, pp. 163-190.
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FEFERMAN, SOLOMON
1958 abstracts. Ordinal logics re-examined and On the strength of ordinal logics, Jour, symbolic logic, vol. 23, pp. 105-106.
1960. Arithmetization of metamathematics in a general setting. Fund, math., vol. 49, pp. 35-92.
1962. Transfinite recursive progressions of axiomatic theories. Jour, symbolic logic, vol. 27, pp. 259-316.
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FRAENKEL, ABRAHAM A. and BAR-HILLEL, YEHOSHUA
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FREGE, GOTTLOB
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1932. Vber die Existenz unabhangiger Axiomensysteme zu unendlichen Satzsystemen.
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1934-5. Untersuchungen iiber das logische Schliessen. Mathematische Zeitschrift, vol. 39, pp. 176-210, 405-431. Fr. tr. by Jean Ladriere (with notes by R. Feys and Ladriere), Recherches sur la deduction logique, Paris (Presses Universitaires de France) 1955, XI+ 170 pp.
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1930. Die Vollstandigkeit der Axiome des logischen Funktionenkalkiils. Monatsh.
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1931-2. Ober Vollstandigkeit und Widerspruchsfreiheit. Ergebnisse eines mathe- matischen Kolloquiums, Heft 3 (for 1930-J, pub. 1932), pp. 12-13.
1931—2b. Eine Eigenschaft der Realisierung des Aussagenkalkiils. Ibid., pp. 20-21.
1932-3. Zur intuitionistischen Arithmetik und Zahlentheorie. Ibid., Heft 4 (for 1931-2, pub. 1933), pp. 34-38. Eng. tr. in Davis 1965, pp. 75-81.
1934. On undecidable propositions of formal mathematical systems. Notes by S. C. Kleene and Barkley Rosser on lectures at the Institute for Advanced Study 1934, mimeographed, Princeton, N.J., 30 pp. Reprinted (with a postscript) in Davis 1965, pp. 39-74.
1934a. Review of Skolem 1933. Zentralblatt fur Mathematik und ihre Grenzgebiete,
vol. 7, pp. 193-194.
1938. The consistency of the axiom of choice and of the generalized continuum-hypothesis. Proc. Nat. Acad. Sci., vol. 24, pp. 556-557.
1939. Consistency-proof for the generalized continuum-hypothesis. Ibid., vol. 25, pp. 220-224.
1940. The consistency of the axiom of choice and of the generalized continuum-hypothesis with the axioms of set theory. Notes by George W. Brown on lectures at the Institute for Advanced Study 1938-9. Annals of Mathematics studies, no. 3, Princeton, N.J. (Princeton Univ. Press), 66 pp. Second printing 1951, v+69 pp.
1947. What is Cantor's continuum problem? American mathematical monthly, vol. 54, pp. 515-525. Reprinted with additions in Benacerraf and Putnam 1964, pp. 258-273.
HALL, MARSHALL, JR.
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HENKIN, LEON
1947. The completeness of formal systems. Ph.D. thesis, Princeton, ii-f 75 pp.
1949. The completeness of the first-order functional calculus. Jour, symbolic logic, vol. 14, pp.'159-166.
1950. Completeness in the theory of types. Ibid., vol. 15, pp. 81-91.
1963. An extension of the Craig-Lyndon interpolation theorem. Ibid., vol. 28, pp. 201-216.
HERBRAND, JACQUES
1928. Sur la theorie de la demonstration. Comptes rendus hebdomadaires des seances de l'Academie des Sciences (Paris), vol. 186, pp. 1274-1276.
1930. Recherches sur la theorie de la demonstration. Travaux de la Societe des Sciences et des Lettres de Varsovie, Classe III sciences mathematiques et physiques, no. 33,128 pp. Eng. tr. of Chapter 5 (extensively annotated) by Burton Dreben and J. van Heijenoort in van Heijenoort 1967.
1931-2. Sur la non-contradiction de Varithmetique. Jour, reine angew. Math., vol. 166, pp. 1-8. Eng. tr. in van Heijenoort 1967.
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1929. Ober Axiomensysteme fur beliebige Satzsysteme. Math. Ann., vol. 101, pp. 457-514.
HEYTING, AREND
1930. Die formalen Regeln der intuitionistischen Logik. Sitz. Preuss. Akad. Wiss., Phys.-math. Kl., 1930, pp. 42-56.
1930a. Die formalen Regeln der intuitionistischen Mathematik. Ibid., pp. 57-71, 158-169.
1934. Mathematische Grundlagenforschung. Intuitionismus. Beweistheorie. Ergeb.
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1955. Les fondements des mathematiques. Intuitionnisme. Theorie de la demonstration.
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1900a. Mathematical problems. Lecture delivered before the International Congress of Mathematicians at Paris in 1900. Eng. tr. from the original Ger., Bull. Amer. Math. Soc, vol. 8 (1901-2), pp. 437-^79. Sur les problemes futurs des mathematiques, Fr. tr. with some modifications and additions, Compte rendus du Deuxieme Congres International des Mathematiciens tenu a Paris du 6 au 12 aout 1900, Paris 1902, pp. 58-114.
1904. Vber die Grundlagen der Logik und der Arithmetik. Verhandlungen des Dritten International Mathematiker-Kongresses in Heidelberg vom 8. bis 13. August 1904, Leipzig 1905, pp. 174-185. Reprinted in 7th ed. of 1899, pp. 247-261. Eng. tr. in van Heijenoort 1967.
1918. Axiomatisches Denken. Math. Ann., vol. 78, pp. 405-415. Reprinted in David Hilbert Gesammelte Abhandlungen, vol. 3, Berlin (Springer) 1935, pp.
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1928. Die Grundlagen der Mathematik. Abhandlungen aus dem Mathematischen Seminar der Hamburgischen Universitat, vol. 6, pp. 65-85. Reprinted with abridgements in 7th ed. of 1899, pp. 289-312. Eng. tr. in van Heijenoort 1967.
HILBERT, DAVID and ACKERMANN, WILHELM
1928, 1938, 1949. Grundzuge der theoretischen Logik. Berlin (Springer), viii+120 pp. 2nd. ed. 1938, viii + 133 pp. Reprinted New York (Dover Pubs.) 1946. 3rd. ed. Berlin, Gottingen, Heidelberg (Springer) 1949, viii+155 pp. Eng. tr. of 2nd. ed., Principles .of mathematical logic, New York (Chelsea Pub. Co.), 1950, xii+172 pp.
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HINTIKKA, K. JAAKKO J.
1955. Form and content in quantification theory. Two papers on symbolic logic, Acta philosophica Fennica no. 8, Helsinki 1955, pp. 7-55.
1955a. Notes on quantification theory. Societas Scientiarum Fennica, Commenta- tiones physico-mathematicae, vol. 17, no. 12, 13 pp.
JASKOWSKI, STANISLAW
1934.On the rules of suppositions in formal logic. Studia logica, no. 1, Warsaw, 32 pp.
1928-9.Eine Bemerkung zur Entscheidungstheorie. Acta litterarum ac scientiarum Regiae Universitatis Hungaricae Francisco-Josephinae, Sectio scientiarum mathe-maticarum (Szeged), vol. 4, pp. 248-252.
1934-5. Uber die Axiomatisierbarkeit des Aussagenkalkuls. Ibid., vol. 7, pp. 222-243.
1959. An argument against the plausibility of Church's thesis. Constructivity in mathematics, Proceedings of the Colloquium held at Amsterdam, [Aug. 26-31] 1957 (A. Heyting, ed.), Amsterdam (North-Holland Pub. Co.), pp. 72-80.
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KLEENE, STEPHEN Cole (also Church and —; — and Post; — and Vesley)
1934. Proof by cases informal logic. Ann. of Math., 2 s., vol. 35, pp. 529-544.
1935. A theory of positive integers informal logic. Amer. jour, math., vol. 57, pp. 153-173, 219-244.
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1936a.^-definability and recursiveness. Duke mathematical journal, vol. 2, pp. 340-353.
1938. On notation for ordinal numbers. Jour, symbolic logic, vol. 3, pp. 150-155.
1943 (abstract 1940).Recursive predicates and quantifiers. Transactions of the American Mathematical Society, vol. 53, pp. 41-73. Reprinted in Davis 1965, pp. 254-287. Abstract in Bull. Amer. Math. Soc, vol. 46, p. 885.
1950. A symmetric form of GodeVs theorem. Kon. Ned. Akad. Wet. (Amsterdam), Proc. Sect. Sci., vol. 53, pp. 800-802 (or Indag. math., vol. 12, pp. 244-246).
1952. Permutability of inferences in Gentzetfs calculi LK and LJ. Two papers on the predicate calculus, by S. C. Kleene (Memoirs Amer. Math. Soc., no. 10), pp. 1-26. In Footnote 15 line 2 "subformula" should be "side formula", and in line 4 the two —I—*'s (or 3—>'s) should have the same principal formula, as noted by G. E. Mine.269 These and other corrections of Two papers are made in the 1957 edition.
1952a. Finite axiomatizability of theories in the predicate calculus using additional predicate symbols, Ibid., pp. 27-68. Amplifications are required on p. 53 (to treat —�3'sand—�&'s belonging to operators inN(x))and helpful on p. 58 middle,as given by G. E. Mine in the Russian tr. of Two papers in Matematiceskaja teorija logiceskogo vyvoda (The mathematical theory of logical inference), Moscow (Nauka) 1967(7).
1952b. Introduction to metamathematics. Amsterdam (North-Holland Pub. Co.), Groningen (Noordhoff), New York and Toronto (Van Nostrand), X+550 pp. Some errata in early printings, and emendations, are listed in Kleene and Vesley 1965 pp. 1, 192 and here in Footnote 86.
1955b. Hierarchies of number-theoretic predicates. Bull. Amer. Math. Soc., vol. 61, pp. 193-213.
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1961. Mathematical logic. Notes by Edward Pols on lectures at a N.S.F. Summer Institute, Bowdoin College, Brunswick, Maine, mimeographed, ix+217 pp.
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