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Some derived rules of intuitionistic second order arithmetic. (English) Zbl 0381.03044


MSC:

03F35 Second- and higher-order arithmetic and fragments
03F55 Intuitionistic mathematics
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References:

[1] A. S. Troelstra: Metamathematical investigation of intuitionistic arithmetic and analysis. Springer Lecture Notes, 344 (1973). · Zbl 0275.02025
[2] A. S. Troelstra: Note on the fan theorem. Journal of Symbolic Logic, 39, 584-597 (1974). JSTOR: · Zbl 0306.02026 · doi:10.2307/2272902
[3] W. A. Howard: Functional interpretation of bar induction by bar recursion, Compositio Mathematica, 20, 107-124 (1968). · Zbl 0162.31503
[4] W. A. Howard and G. Kreisel: Transfinite induction and bar induction of type zero and one, and the role of continuity in intuitionistic analysis. Journal of Symbolic Logic, 31, 325-358 (1966). JSTOR: · Zbl 0156.00804 · doi:10.2307/2270450
[5] P. Martin-Lof: Hauptsatz for the intuitionistic theory of iterated inductive defenitions. Proceedings of the Second Scandinavian Logic Symposium, North-Holland, 179-216 (1971). · Zbl 0231.02040
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