Coinductive well-foundedness

We introduce a coinductive version of the well-foundedness of N that is used in our proof within minimal logic of the constructive counterpart CLNP to the standard least number principle LNP. According to CLNP, an inhabited complemented subset of N has a least element if and only if it is downset lo...

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Bibliographic Details
Main Author Petrakis, Iosif
Format Journal Article
LanguageEnglish
Published 01.07.2025
Subjects
Mathematics - Logic
Online AccessGet full text
DOI10.48550/arxiv.2506.16433

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Summary:We introduce a coinductive version of the well-foundedness of N that is used in our proof within minimal logic of the constructive counterpart CLNP to the standard least number principle LNP. According to CLNP, an inhabited complemented subset of N has a least element if and only if it is downset located. The use of complemented subsets of N in the formulation of CLNP, instead of subsets of N, allows a positive approach to the subject that avoids negation. Generalising the coinductive well-foundedness of N, we define $\exists$-well-founded sets and we prove their fundamental properties.
DOI:10.48550/arxiv.2506.16433