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A Tale of Two Set Theories

07/18/2019

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by Chad E. Brown, et al.

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We describe the relationship between two versions of Tarski-Grothendieck set theory: the first-order set theory of Mizar and the higher-order set theory of Egal. We show how certain higher-order terms and propositions in Egal have equivalent first-order presentations. We then prove Tarski's Axiom A (an axiom in Mizar) in Egal and construct a Grothendieck Universe operator (a primitive with axioms in Egal) in Mizar.

Chad E. Brown
8 publications
Karol Pąk
2 publications

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