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End extending models of set theory via power admissible covers
McKenzie, Zachiri Enayat, Ali
McKenzie, Zachiri
Enayat, Ali
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2022-04-15
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Abstract
Motivated by problems involving end extensions of models of set theory, we develop the rudiments of the power admissible cover construction (over ill-founded models of set theory), an extension of the machinery of admissible covers invented by Barwise as a versatile tool for generalising model-theoretic results about countable well-founded models of set theory to countable ill-founded ones. Our development of the power admissible machinery allows us to obtain new results concerning powerset-preserving end extensions and rank extensions of countable models of subsystems of ZFC . The canonical extension KP P of Kripke-Platek set theory KP plays a key role in our work; one of our results refines a theorem of Rathjen by showing that Σ 1 P -Foundation is provable in KP P (without invoking the axiom of choice).
Citation
McKenzie, Z., & Enayat, A. (2022). End extending models of set theory via power admissible covers. Annals of Pure and Applied Logic, 173(8), article-number 103132. https://doi.org/10.1016/j.apal.2022.103132
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Elsevier
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Annals of Pure and Applied Logic
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DOI
10.1016/j.apal.2022.103132
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Article
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en
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© 2022 The Author(s). Published by Elsevier B.V.
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0168-0072
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1873-2461
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