The Type Theoretic Interpretation of Constructive Set Theory"
نویسندگان
چکیده
INTRODUCTION Intuitionistic mathematics can be structured into two levels. The first level arises directly out of Brouwer's criticism of certain methods and notions of classical mathematics. the law of excluded middle was rejected and instead the meaning of mathematical statements was to be based on the notion of 'proof'. level of intuitionism was a theory of meaning quite different from the classical one, it was nevertheless the case that the body of mathematics that could be developed within this level remained a part of classical mathematics. Brouwer felt that Mathematical analysis could not be developed adequately on this basis he was led to formulate his own conception of the continuum. conception involved the mathematical treatment of incompletely specified objects such as free choice sequences. first level but also includes these radical ideas that turn out to be incompatible with classical mathematics. years to make these ideas more transparent they have remained rather obscure to w s t mathematicians and the mathematics based on them has had a very limited following. In particular the notion of 'truth' that gives rise to
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