About Goodmanʼs Theorem

Annals of Pure and Applied Logic 164 (4):437-442 (2013)
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Abstract

We present a proof of Goodmanʼs Theorem, which is a variation of the proof of Renaldel de Lavalette [9]. This proof uses in an essential way possibly divergent computations for proving a result which mentions systems involving only terminating computations. Our proof is carried out in a constructive metalanguage. This involves implicitly a covering relation over arbitrary posets in formal topology, which occurs in forcing in set theory in a classical framework, but can also be defined constructively

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Citations of this work

On Goodman Realizability.Emanuele Frittaion - 2019 - Notre Dame Journal of Formal Logic 60 (3):523-550.

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References found in this work

Pretopologies and completeness proofs.Giovanni Sambin - 1995 - Journal of Symbolic Logic 60 (3):861-878.
Proof-theoretical analysis: weak systems of functions and classes.L. Gordeev - 1988 - Annals of Pure and Applied Logic 38 (1):1-121.
A semantical proof of De Jongh's theorem.Jaap van Oosten - 1991 - Archive for Mathematical Logic 31 (2):105-114.
Extended bar induction in applicative theories.G. R. Renardel Delavalette - 1990 - Annals of Pure and Applied Logic 50 (2):139-189.

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