Pour-El's Landscape

Taishi Kurahashi; Albert Visser

doi:10.48550/arXiv.2310.04814

Pour-El's Landscape

Research output: Working paper › Preprint › Academic

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.

Original language	English
Publisher	arXiv
Number of pages	35
DOIs	https://doi.org/10.48550/arXiv.2310.04814
Publication status	Published - 7 Oct 2023

Keywords

math.LO
03F25, 03F30, 03F40

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10.48550/arXiv.2310.04814Licence: CC BY

2310.04814v1Submitted manuscript, 387 KBLicence: CC BY

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Pour-El's Landscape

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Keywords

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