Intuitionist type theory and foundations

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Journal of Philosophical Logic 10 (1):101 - 115 (1981)
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Abstract

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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10.1007/bf00253914

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Category theory.Jean-Pierre Marquis - 2008 - Stanford Encyclopedia of Philosophy.

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References found in this work

Introduction to metamathematics.Stephen Cole Kleene - 1952 - Groningen: P. Noordhoff N.V..
Natural deduction: a proof-theoretical study.Dag Prawitz - 1965 - Mineola, N.Y.: Dover Publications.
Mathematical Logic as Based on the Theory of Types.Bertrand Russell - 1908 - American Journal of Mathematics 30 (3):222-262.
Completeness in the theory of types.Leon Henkin - 1950 - Journal of Symbolic Logic 15 (2):81-91.
Completeness in the Theory of Types.Leon Henkin - 1950 - Journal of Symbolic Logic 16 (1):72-73.

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