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Weak systems of set theory related to HOL

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Book cover Higher Order Logic Theorem Proving and Its Applications (HUG 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 859))

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Abstract

This is an early version of a survey article designed for the interested non-specialist, and it does not contain any proofs of novel results, though it does contain announcements (of novel unpublished results) and proofs (of frequently underregarded trivialities). For the reader who wishes to take this material further, the chief advantage of this essay will be the bibliography, which would be quite hard for a naïve reader to assemble from scratch. I would like to thank my friend and colleague Juanito Camilleri for the invitation which led to me writing this.

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References

  • Barwise, J. [1975] Admissible sets and structures, an approach to definablity theory. Springer-Verlag 1975.

    Google Scholar 

  • Buchholz, W. and Wainer S. [1985] Provably computable functions and the fast-growing hierarchy. Logic and Combinatorics, AMS Contemporary Mathematics v 65 pp 179–198.

    Google Scholar 

  • Church, A. [1940] A formulation of the simple theory of types. Journal of Symbolic Logic 5 pp. 56–68.

    Google Scholar 

  • Coret, J. [1970] Sur les cas stratifiés du schema de remplacement. Comptes Rendues hebdomadaires des séances de l'Académie des Sciences de Paris série A 271 pp. 57–60.

    Google Scholar 

  • Forster, T.E. [1989] A second-order theory without a (second-order) model. Zeitschrift für mathematische Logik und Grundlagen der Mathematik 35 pp. 285–6

    Google Scholar 

  • Forster, T.E. and Kaye, R.W. [1991] End-extensions preserving power set. Journal of Symbolic Logic 56 pp. 323–28.

    Google Scholar 

  • Forster, T.E. and Kaye, R.W. [2???] More on the set theory KF. unpublished typescript 24pp.

    Google Scholar 

  • Holmes, M.R. [1995] The equivalence of NF-style set theories with “tangled” type theories; the construction of ω-models of predicative NF (and more) Journal of Symbolic Logic to appear

    Google Scholar 

  • Jensen, R.B. [1969] On the consistency of a slight(?) modification of Quine's NF. Synthese 19 pp. 250–63.

    Google Scholar 

  • Kaye, R.W. [1991] A generalisation of Specker's theorem on typical ambiguity. Journal of Symbolic Logic 56 pp 458–466

    Google Scholar 

  • Kemeny, J. [1949] Type theory vs. Set theory. Ph.D.Thesis, Princeton 1949

    Google Scholar 

  • Lake, J. [1975] Comparing Type theory and Set theory. Zeitschrift für Matematischer Logik 21 pp 355–6.

    Google Scholar 

  • Levy, A. [1965] A hierarchy of formulæ in set theory. Memoirs of the American Mathematical Society no 57, 1965.

    Google Scholar 

  • Mathias, A.R.D. [2???] Notes on MacLane Set Theory. unpublished typescript.

    Google Scholar 

  • McNaughton, R. [1953] Some formal relative consistency proofs. Journal of Symbolic Logic 18 pp. 136–44.

    Google Scholar 

  • Mostowski, A. [1950] Some impredicative definitions in the axiomatic set theory. Fundamenta Mathematicæ v 37 pp 111–124.

    Google Scholar 

  • Novak, I.L. [1950] A construction of models for consistent systems. Fundamenta Mathematicæ 37 pp 87–110

    Google Scholar 

  • Quine, W.v.O. [1951] Mathematical Logic. (2nd ed.) Harvard.

    Google Scholar 

  • Quine, W.v.O [1966] On a application of Tarski's definition of Truth. in Selected Logic Papers pp 141–5

    Google Scholar 

  • Rosser, J.B. and Wang, H. [1950] Non-standard models for formal logics JSL 15 pp 113–129

    Google Scholar 

  • Scott, D. S. [1960] Review of Specker [1958]. Mathematical Reviews 21 p. 1026.

    Google Scholar 

  • Shoenfield, J. R. [1954] A relative consistency proof Journal of Symbolic Logic 19 pp 21–28

    Google Scholar 

  • Specker, E. P. [1958] Dualität. Dialectica 12 pp. 451–465.

    Google Scholar 

  • Specker, E. P. [1962] Typical ambiguity. In Logic, methodology and philosophy of science. Ed E. Nagel, Stanford.

    Google Scholar 

  • Wang, H. [1949] On Zermelo's and Von Neumann's axioms for set theory. Proc. N. A. S. 35 pp 150–155

    Google Scholar 

  • Wang, H. [1952] Truth definitions and consistency proofs. Transactions of the American Mathematical Society 72 pp. 243–75. reprinted in Wang: Survey of Mathematical Logic as ch 18

    Google Scholar 

  • Wang, H. [1952a] Negative types. MIND 61 pp. 366–8.

    Google Scholar 

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Authors and Affiliations

  1. D.P.M.M.S., University of Cambridge, UK

    Thomas Forster

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  1. Thomas Forster
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Thomas F. Melham Juanito Camilleri

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© 1994 Springer-Verlag Berlin Heidelberg

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Forster, T. (1994). Weak systems of set theory related to HOL. In: Melham, T.F., Camilleri, J. (eds) Higher Order Logic Theorem Proving and Its Applications. HUG 1994. Lecture Notes in Computer Science, vol 859. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58450-1_43

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  • DOI: https://doi.org/10.1007/3-540-58450-1_43

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58450-6

  • Online ISBN: 978-3-540-48803-3

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