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A topological interpretation of second-order intuitionistic arithmetic. (English) Zbl 0279.02018

MSC:
03F55 Intuitionistic mathematics
03C99 Model theory
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References:
[1] S.C. Kleene and R.E. Vesley [1] The Foundations of intuitionistic mathematics , Amsterdam (North-Holland), 1965. · Zbl 0133.24601
[2] G. Kreisel and A.S. Troelstra [2] Formal systems for some branches of intuitionistic analysis , Annals of mathematical logic, Vol. 1 (1970), pp. 229-387. · Zbl 0211.01101 · doi:10.1016/0003-4843(70)90001-X
[3] G. Kreisel [3] Informal rigour and completeness proofs, in Problems in the philosophy of mathematics , ed. I. LAKATOS, Amsterdam (North-Holland), 1967, pp. 138-171, with following discussion.
[4] J.R. Moschovakis [4] Disjunction, existence, and \lambda -definability in formalized intuitionistic analysis , Ph. D. Thesis, University of Wisconsin, 1965.
[5] J. Myhill [5] Formal systems of intuitionistic analysis I, in Logic, methodology and philosophy of science III , eds. B. van Rootselaar and J. F. Staal, Amsterdam (North-Holland), 1968, pp. 161-178. · Zbl 0202.00601
[6] H. Rasiowa and R. Sikorski [6] The mathematics of metamathematics , Warsaw, 1963. · Zbl 0122.24311
[7] D. Scott [7] Extending the topological interpretation to intuitionistic analysis , Compositio Mathematica 20 (1968), pp. 194-210. · Zbl 0197.00201 · numdam:CM_1968__20__194_0 · eudml:88978
[8] D. Scott [8] Extending the topological interpretation to intuitionistic analysis II, in Intuitionism and proof theory , eds. J. Myhill, A. Kino and R. Vesley, Amsterdam (North-Holland), 1970, pp. 235-255. · Zbl 0213.01203
[9] A.S. Troelstra Notes on the intuitionistic theory of sequences (I) , Indag. Math. 31, No. 5 (1969). · Zbl 0188.31603
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