a brouwerian proof of the fan theorem
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A Brouwerian Proof of the Fan theorem Michael P . Fourman - PowerPoint PPT Presentation

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A Brouwerian Proof of the Fan theorem Michael P . Fourman dedicated to Dana S. Scott section x x = id B E open U fibre B t slides presented at domains13, Oxford 7/7/2018; with minor modifications 9/7/2018 the topological

  1. A Brouwerian Proof of the Fan theorem Michael P . Fourman dedicated to Dana S. Scott section x x π = id B E open U π fibre B t slides presented at domains13, Oxford 7/7/2018; with minor modifications 9/7/2018

  2. the topological interpretation Extending to intuitionistic analysis his 70th birthday Dedicated to A. Heyting on the occasion of by Dana Scott Compositio Mathematica , tome 20 (1968), p. 194-210. well-known Stone-Tarski intuitionistic The of the interpretation 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 difficulty in verifying certain of the continuity some F4 of [6] for Voc3fJ to be précise) and assumptions (Axiom hopes understand the motivation behind these principles better to to try before presenting the details of the model. It is not impossible that there are several distinct intuitionistic notions of free-choice with various continuity properties. sequence (real number)

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