Weak systems of set theory related to HOL
- Thomas Forster
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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non-specialist, and it does not contain any proofs of novel results, though it does contain announcements (of novel unpublished results) and proofs (of frequently underregarded trivialities).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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- Church, A.  A formulation of the simple theory of types. Journal of Symbolic Logic 5 pp. 56–68.
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- Forster, T.E.  A second-order theory without a (second-order) model. Zeitschrift für mathematische Logik und Grundlagen der Mathematik 35 pp. 285–6
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- Forster, T.E. and Kaye, R.W. [2???] More on the set theory KF. unpublished typescript 24pp.
- Holmes, M.R.  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
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- Kaye, R.W.  A generalisation of Specker's theorem on typical ambiguity. Journal of Symbolic Logic 56 pp 458–466
- Kemeny, J.  Type theory vs. Set theory. Ph.D.Thesis, Princeton 1949
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- Novak, I.L.  A construction of models for consistent systems. Fundamenta Mathematicæ 37 pp 87–110
- Quine, W.v.O.  Mathematical Logic. (2nd ed.) Harvard.
- Quine, W.v.O  On a application of Tarski's definition of Truth. in Selected Logic Papers pp 141–5
- Rosser, J.B. and Wang, H.  Non-standard models for formal logics JSL 15 pp 113–129
- Scott, D. S.  Review of Specker . Mathematical Reviews 21 p. 1026.
- Shoenfield, J. R.  A relative consistency proof Journal of Symbolic Logic 19 pp 21–28
- Specker, E. P.  Dualität. Dialectica 12 pp. 451–465.
- Specker, E. P.  Typical ambiguity. In Logic, methodology and philosophy of science. Ed E. Nagel, Stanford.
- Wang, H.  On Zermelo's and Von Neumann's axioms for set theory. Proc. N. A. S. 35 pp 150–155
- Wang, H.  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
- Wang, H. [1952a] Negative types. MIND 61 pp. 366–8.
- Weak systems of set theory related to HOL
- Book Title
- Higher Order Logic Theorem Proving and Its Applications
- Book Subtitle
- 7th International Workshop Valletta, Malta, September 19–22, 1994 Proceedings
- pp 193-204
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- Lecture Notes in Computer Science
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- Springer Berlin Heidelberg
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