On second order logic
Part of : Philosophical inquiry ; Vol.39, No.1, 2015, pages 59-62
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59-62
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References (1):
- [I] Paul Cohen. The independence of the continuum hypothesis. Proc. Nat. Acad. Sci. U.S.A., 50:1143-1148, 1963.[2] Kurt Godei. The consistency of the axiom of choice and of the generalized continuum- hypothesis. Proc. Natl. Acad. Sci. USA, 24:556-557, 1938.[3] Leon Henkin. Completeness in the theory of types. J. Symbolic Logic, 15:81-91, 1950.[4] D. Hilbert and W. Ackermann. Grundzuge der theoretischen Logik. Berlin: J. Springer (Die Grundlehren der mathematischen Wis senschaften Bd. 27). VIII, 120 S. (1928)., 1928.[5] E. V. Huntington. A complete set of postulates for the theory of of absolute continuous magnitude.[6] Tapani Hyttinen, Kaisa Kangas, and Jouko Vaananen. On second-order characterizability. Log. J. IGPL, 21(5):767-787, 2013.[7] G. Kreisel. Informal rigour and completeness proofs. In Proceedings of the International Colloquium in the Philosophy of Science, London, 1965, Vol. 1. Edited by Imre Lakatos, pages 138-157. North-Holland Publishing Co., Amsterdam, 1967.[8] Alfred Tarski. Der Wahrheitsbegriff in den Sprachen der deduktiven Disziplinen. Anzeiger Wien, 69:23-25, 1932.[9] Jouko Vaananen. Abstract logic and set theory. I. Definability. Logic colloquium '78, Proc, Mons/Belgium 1978, Stud. Logic Found. Math. Vol. 97, 391-421 (1979)., 1979.[10] Jouko Vaananen. Second-order logic and foundations of mathematics. Bull. Symbolic Logic, 7(4):504-520, 2001.[II] Jouko Vaananen. Second order logic or set theory? Bull. Symbolic Logic, 18(1):91-121,2012.Jouko Vaananen and Tong Wang. Internal categoricity in arithmetic and set theory. Notre Dame Journal of Formal Logic, to appear.
