A variety of partially conservative sentences
Haruka Kogure, Taishi Kurahashi

TL;DR
This paper investigates the existence of sentences that are conservative over different extensions of Peano Arithmetic, providing affirmative answers to longstanding questions about their properties and existence.
Contribution
It proves the existence of sentences that are hereditarily conservative over any single theory, answering Guaspari's question affirmatively.
Findings
Existence of $ heta$ sentences that are $ heta$-conservative over various theories
Existence of sentences that are hereditarily $ heta$-conservative over any single theory
Affirmative resolution of Guaspari's question about conservative sentences
Abstract
We study the existence of a sentence which is simultaneously -conservative over consistent RE extensions and of Peano Arithmetic for various reasonable pairs . As a result of this study, we prove the existence of a sentence which is essentially and exactly hereditarily -conservative over any single theory for various reasonable pairs . This is an affirmative answer to Guaspari's question.
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Taxonomy
TopicsLanguage, Discourse, Communication Strategies
