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Extending the topological interpretation to intuitionistic analysis

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  • Law
  • Logic
  • Mathematics

Abstract

Extending the topological interpretation to intuitionistic analysis COMPOSITIO MATHEMATICA DANA SCOTT Extending the topological interpretation to intuitionistic analysis Compositio Mathematica, tome 20 (1968), p. 194-210. <http://www.numdam.org/item?id=CM_1968__20__194_0> © Foundation Compositio Mathematica, 1968, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http:// http://www.compositio.nl/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commer- ciale ou impression systématique est constitutive d’une infraction pé- nale. Toute copie ou impression de ce fichier doit contenir la pré- sente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ 194 Extending the topological interpretation to intuitionistic analysis Dedicated to A. Heyting on the occasion of his 70th birthday by Dana Scott The well-known Stone-Tarski interpretation of the intuitionistic propositional logic was extended by Mostowski to the quantifier logic in a natural way. For details and references the reader may consult the work Rasiowa-Sikorski [5], where intuitionistic theories are discussed in general, but where no particular theory is analysed from this point of view. The purpose of this paper is to present some classically interesting models for the intuition- istic theory of the continuum. These models will be applied to some simple independence questions. The idea of the model can also be used for models of second-order intuitionistic arithmetic (cf. the system of [6]), but lack of time and space force us to postpone this discussion to another paper. Also, the author has encountered some difficulty in verifying certain of the continuity assumptions (Axiom F4 of [6] for Voc3fJ to be précise) and hopes to try to understand the motivation behind these principles better before presenting the details of the m

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