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Claim

First Principles of Mathematics

descriptionPublicationkeyboard_double_arrow_right Book 15 Nov 2022 English Publisher:Zenodo
Authors: Taylor, Forrest C.;

doi: 10.5281/zenodo.7882535 , 10.5281/zenodo.7771088 , 10.5281/zenodo.7780699 , 10.5281/zenodo.7582225 , 10.5281/zenodo.7792586 , 10.5281/zenodo.7817717 , 10.5281/zenodo.7905338 , 10.5281/zenodo.7817868 , 10.5281/zenodo.7826762 , 10.5281/zenodo.7814785 , 10.5281/zenodo.7780759 , 10.5281/zenodo.7321993 , 10.5281/zenodo.7902037 , 10.5281/zenodo.7826593 , 10.5281/zenodo.7765158 , 10.5281/zenodo.7668941 , 10.5281/zenodo.7903290 , 10.5281/zenodo.7875657 , 10.5281/zenodo.7321992

First Principles of Mathematics

Abstract

A dependent type theory is proposed as the foundation of mathematics. The formalism preserves the structure of mathematical thought, making it natural to use. The logical calculus of the type theory is proved to be syntactically complete. Therefore it does not suffer from the limitations imposed by Gödel’s incompleteness theorems. In particular, the concept of mathematical truth can be defined in terms of provability.

Keywords

logic, foundations of mathematics, incompleteness theorem, mathematics, truth, first principles, Euclid, foundations, Elements, Martin-Löf type theory, Gödel's incompleteness theorem, mathematical truth, type theory, rigorous, mathematical logic, first principles of mathematics

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