Truth definitions and consistency proofs
HTML articles powered by AMS MathViewer
- by Hao Wang PDF
- Trans. Amer. Math. Soc. 73 (1952), 243-275 Request permission
References
- Paul Bernays, A system of axiomatic set theory. Part II, J. Symbolic Logic 6 (1941), 1–17. MR 3382, DOI 10.2307/2267281
- Kurt Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatsh. Math. Phys. 38 (1931), no. 1, 173–198 (German). MR 1549910, DOI 10.1007/BF01700692 David Hilbert and Paul Bernays Grundlagen der Mathematik, vol. 1, 1934, vol. 2, 1939, Berlin, Springer.
- Leon Henkin, A generalization of the concept of $\omega$-completeness, J. Symbolic Logic 22 (1957), 1–14. MR 95120, DOI 10.2307/2964052
- Leon Henkin, Completeness in the theory of types, J. Symbolic Logic 15 (1950), 81–91. MR 36188, DOI 10.2307/2266967 A. Malcev Untersuchungen aus dem Gebiete der mathematischen Logik, Recueil Mathématique N.S. vol. 1 (1936) pp. 323-336. John von Neumann Zur Einführung der transfiniten Zahlen, Acta litterarum ac scientiarum Regiae Universitatis Hungaricae Francisco-Josephinae, Sectio scientiarum mathematicarum vol. 1 (1923) pp. 199-208.
- I. L. Novak, A construction for models of consistent systems, Fund. Math. 37 (1950), 87–110. MR 41082, DOI 10.4064/fm-37-1-87-110 John G. Kemeny Type theory vs. set theory, a Thesis at Princeton University (1949). (Abstract appeared on p. 78 of J. Symbolic Logic vol. 15 (1950)). W. V. Quine Mathematical logic, New York, 1940; second printing, Cambridge, Mass., 1947.
- W. V. Quine, Element and number, J. Symbolic Logic 6 (1941), 135–149. MR 6326, DOI 10.2307/2267106
- J. Barkley Rosser and Hao Wang, Non-standard models for formal logics, J. Symbolic Logic 15 (1950), 113–129. MR 38307, DOI 10.2307/2266971
- Arnold Schmidt, Über deduktive Theorien mit mehreren Sorten von Grunddingen, Math. Ann. 115 (1938), no. 1, 485–506 (German). MR 1513200, DOI 10.1007/BF01448954 Thoralf Skolem Über einige Grundlagenfragen der Mathematik, Skrifter utgitt av Det. Norske Viden-skaps-Akademi, I, no. 4, 1929, 49 pp. —Über die Nicht-charakterisierbarkeit der Zahlenreihe mittels endlich oder abzählbar unendlich vieler Aussagen mit ausschliesslich Zahlenvariablen, Fund. Math. vol. 23 (1934) pp. 150-161. Alfred Tarski Der Wahrheitsbegriff in den formalisierten Sprachen, Studia Philosophica vol. 1 (1936) pp. 261-405. (Original in Polish, 1933.)
- Alfred Tarski, On undecidable statements in enlarged systems of logic and the concept of truth, J. Symbolic Logic 4 (1939), 105–112. MR 210, DOI 10.2307/2266444
- Alfred Tarski, The semantic conception of truth and the foundations of semantics, Philos. and Phenomenol. Res. 4 (1944), 341–376. MR 10521
- Hao Wang, A new theory of element and number, J. Symbolic Logic 13 (1948), 129–137. MR 26978, DOI 10.2307/2267813
- Hao Wang, On Zermelo’s and von Neumann’s axioms for set theory, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), 150–155. MR 29850, DOI 10.1073/pnas.35.3.150
- Hao Wang, Remarks on the comparison of axiom systems, Proc. Nat. Acad. Sci. U.S.A. 36 (1950), 448–453. MR 39661, DOI 10.1073/pnas.36.8.448
- Hao Wang, Arithmetic translations of axiom systems, Trans. Amer. Math. Soc. 71 (1951), 283–293. MR 43046, DOI 10.1090/S0002-9947-1951-0043046-1
Additional Information
- © Copyright 1952 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 73 (1952), 243-275
- MSC: Primary 02.0X
- DOI: https://doi.org/10.1090/S0002-9947-1952-0049136-2
- MathSciNet review: 0049136