Intuitionist type theory and foundations

Journal of Philosophical Logic 10 (1):101 - 115 (1981)
A version of intuitionistic type theory is presented here in which all logical symbols are defined in terms of equality. This language is used to construct the so-called free topos with natural number object. It is argued that the free topos may be regarded as the universe of mathematics from an intuitionist's point of view
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