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arXiv · 2412.08208

A variety of partially conservative sentences

Haruka Kogure·Taishi Kurahashi
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Abstract

We study the existence of a $\Theta$ sentence which is simultaneously $\Gamma$-conservative over consistent RE extensions $T$ and $U$ of Peano Arithmetic for various reasonable pairs $(\Gamma, \Theta)$. As a result of this study, we prove the existence of a sentence which is essentially $\Theta$ and exactly hereditarily $\Gamma$-conservative over any single theory $T$ for various reasonable pairs $(\Gamma, \Theta)$. This is an affirmative answer to Guaspari's question.

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Haruka Kogure, Taishi Kurahashi. 2024-12-11. A variety of partially conservative sentences. https://arxiv.org/abs/2412.08208

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