2025/06/19 by Petrakis, Iosif
Computer Science · #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.2506.16433
openalex publication_date 2025/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ∃-well-founded sets and we prove their fundamental properties.