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  1. Analyzing realizability by Troelstra's methods.Joan Rand Moschovakis - 2002 - Annals of Pure and Applied Logic 114 (1-3):203-225.
    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 (...)
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