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Axiom of Choice and Excluded Middle in Categorical Logic
 Bulletin of Symbolic Logic
, 1995
"... The axiom of choice is shown to hold in the predicative logic of any locally cartesian closed category. A predicative form of excluded middle is then shown to be equivalent to the usual form of choice in topoi. ..."
Abstract

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The axiom of choice is shown to hold in the predicative logic of any locally cartesian closed category. A predicative form of excluded middle is then shown to be equivalent to the usual form of choice in topoi.
MATHEMATICAL LOGIC QUARTERLY
, 2007
"... The axiomofchoice and the law of excluded middle in weak set theories ..."
TYPES, SETS AND CATEGORIES
"... This essay is an attempt to sketch the evolution of type theory from its beginnings early in the last century to the present day. Central to the development of the type concept has been its close relationship with set theory to begin with and later its even more intimate relationship with category t ..."
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This essay is an attempt to sketch the evolution of type theory from its beginnings early in the last century to the present day. Central to the development of the type concept has been its close relationship with set theory to begin with and later its even more intimate relationship with category theory. Since it is effectively impossible to describe these relationships (especially in regard to the latter) with any pretensions to completeness within the space of a comparatively short article, I have elected to offer detailed technical presentations of just a few important instances. 1 THE ORIGINS OF TYPE THEORY The roots of type theory lie in set theory, to be precise, in Bertrand Russellâ€™s efforts to resolve the paradoxes besetting set theory at the end of the 19 th century. In analyzing these paradoxes Russell had come to find the set, or class, concept itself philosophically perplexing, and the theory of types can be seen as the outcome of his struggle to resolve these perplexities. But at first he seems to have regarded type theory as little more than a faute de mieux.