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Axiom Selection by Maximization: V = Ultimate L vs Forcing Axioms
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| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | Axiom Selection by Maximization: V = Ultimate L vs Forcing Axioms. |
| 개인저자 | Schatz, Jeffrey Robert. |
| 단체저자명 | University of California, Irvine. Philosophy - Ph.D.. |
| 발행사항 | [S.l.]: University of California, Irvine., 2019. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2019. |
| 형태사항 | 110 p. |
| 기본자료 저록 | Dissertations Abstracts International 81-04B. Dissertation Abstract International |
| ISBN | 9781687997562 |
| 학위논문주기 | Thesis (Ph.D.)--University of California, Irvine, 2019. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
Advisor: Maddy, Penelope. |
| 이용제한사항 | This item must not be sold to any third party vendors. |
| 요약 | This dissertation explores the justi詮갷ation of strong theories of sets extending Zeremelo-Fraenkel set theory with choice and large cardinal axioms. In particular, there are two noted program providing axioms extending this theory: the inner model program and the forcing axiom program. While these programs historically developed to serve different mathematical goals and ends, proponents of each have attempted to justify their preferred axiom candidate on the basis of its supposed maximization potential. Since the maxim of 'maximize' proves central to the justi詮갷ation of ZFC+LCs itself, and shows up centrally in the current debate over how to best extend this theory, any attempt to resolve this debate will need to investigate the relationship between maximization notions and the candidates for a strong theory of sets. This dissertation takes up just this project.The 詮걊st chapter of this dissertation describes the history of axiom selection in set theory, focusing on developments since 1980 which have led to the two standard axiom candidates for extending ZFC+LCs: V = Ult(L) and Martin's Maximum. The second chapter explains the justi詮갷ation of the methodological maxim of 'maximize' as an informal principle, and presents two formal explications of the notion: one due to John Steel, the other to Penelope Maddy. The third chapter directly examines whether either approach to axioms can be truly said to maximize over the other. It is shown that the axiom candidates are equivalent in Steel's sense of 'maximize', while in Maddy's sense of 'maximize', Martin's Maximum is found to maximize over V = Ult(L). Given the strong justi詮갷ation of Maddy's explication in terms of the goals of set theory as a foundational discipline, it is argued that this result raises a serious justi詮갷atory challenge for advocates of the inner model program. The fourth chapter considers future directions of research, focusing on possible responses to the justi詮갷atory challenge, and highlighting issues that must be overcome before a full justi詮갷atory story of forcing axioms can be developed. |
| 일반주제명 | Philosophy. Logic. Mathematics. |
| 언어 | 영어 |
| 바로가기 | 
: 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
