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