Annals of Pure and Applied Logic 114 (1-3):203-225 (2002)

Joan Rand Moschovakis
Occidental College
Realizabilities are powerful tools for establishing consistency and independence results for theories based on intuitionistic logic. Troelstra discovered principles ECT 0 and GC 1 which precisely characterize formal number and function realizability for intuitionistic arithmetic and analysis, respectively. Building on Troelstra's results and using his methods, we introduce the notions of Church domain and domain of continuity in order to demonstrate the optimality of “almost negativity” in ECT 0 and GC 1 ; strengthen “double negation shift” DNS 0 to DNS 1 and use it with GC 1 and Markov's Principle MP to characterize the classically provably realizable formulas of analysis; and show that intuitionistic analysis with GC 1 , MP and DNS 1 is consistent and satisfies Troelstra's and Church's Rules. We end with a discussion of semi-intuitionistic theories and a conjecture
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DOI 10.1016/s0168-0072(01)00080-x
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References found in this work BETA

Formal Systems for Some Branches of Intuitionistic Analysis.G. Kreisel - 1970 - Annals of Pure and Applied Logic 1 (3):229.
On the Interpretation of Intuitionistic Number Theory.S. C. Kleene - 1945 - Journal of Symbolic Logic 10 (4):109-124.
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Realizability.A. S. Troelstra - 2000 - Bulletin of Symbolic Logic 6 (4):470-471.
Some Applications of Kleene's Methods for Intuitionistic Systems.Harvey Friedman - 1973 - In A. R. D. Mathias & H. Rogers (eds.), Cambridge Summer School in Mathematical Logic. New York: Springer Verlag. pp. 113--170.

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