Equality and equivalence, intuitionistically
Wim Veldman
TL;DR
This paper investigates the structure of intuitionistic equality and equivalence relations, revealing the existence of many complete extensions and versions within an intuitionistic framework.
Contribution
It demonstrates that the intuitionistic first-order theory of equality has continuum many complete extensions and explores multiple intuitionistic versions of the Vitali equivalence relation.
Findings
Existence of continuum many complete extensions of the theory of equality.
Multiple intuitionistic versions of the Vitali equivalence relation.
Insights into the structure of intuitionistic equality and equivalence relations.
Abstract
We show that the intuitionistic first-order theory of equality has continuum many complete extensions. We also study the Vitali equivalence relation and show there are many intuitionistically precise versions of it.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Mathematical and Theoretical Analysis · History and Theory of Mathematics