English

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

Logic 2020-06-02 v1

Abstract

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

Keywords

Cite

@article{arxiv.2006.01057,
  title  = {How the Law of Excluded Middle Pertains to the Second Incompleteness Theorem and its Boundary-Case Exceptions},
  author = {Dan E. Willard},
  journal= {arXiv preprint arXiv:2006.01057},
  year   = {2020}
}

Comments

Short conference announcements of these results at ASL-2020's Virtual N. American Meeting and at LFCS-2020