How the Law of Excluded Middle Pertains to the Second Incompleteness\n Theorem and its Boundary-Case Exceptions

2020/06/01 by Dan E. Willard, Willard, Dan E.
Computer Science · #03F25 #03F30 #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems

paper · pdf · doi:10.48550/arxiv.2006.01057

openalex publication_date 2020/06/01 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

Our earlier publications showed semantic tableau admits partial exceptions to\nthe Second Incompleteness Theorem where a formalism recognizes its self\nconsistency and views multiplication as a 3-way relation (rather than as a\ntotal function). We now show these boundary-case evasions will collapse if the\nLaw of the Excluded Middle is treated by tableau as a schema of logical axioms\n(instead of as derived theorems).\n

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