English

Pour-El's Landscape

Logic 2024-06-03 v2

Abstract

We study the effective versions of several notions related to incompleteness, undecidability and inseparability along the lines of Pour-El's insights. Firstly, we strengthen Pour-El's theorem on the equivalence between effective essential incompleteness and effective inseparability. Secondly, we compare the notions obtained by restricting that of effective essential incompleteness to intensional finite extensions and extensional finite extensions. Finally, we study the combination of effectiveness and hereditariness, and prove an adapted version of Pour-El's result for this combination.

Keywords

Cite

@article{arxiv.2310.04814,
  title  = {Pour-El's Landscape},
  author = {Taishi Kurahashi and Albert Visser},
  journal= {arXiv preprint arXiv:2310.04814},
  year   = {2024}
}

Comments

36 pages

R2 v1 2026-06-28T12:43:23.864Z