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The Ultrapower Axiom.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	The Ultrapower Axiom./
作者:	Goldberg, Gabriel.
面頁冊數:	1 online resource (423 pages)
附註:	Source: Dissertations Abstracts International, Volume: 82-05, Section: B.
Contained By:	Dissertations Abstracts International82-05B.
標題:	Mathematics. -
電子資源:	click for full text (PQDT)
ISBN:	9798684610455

The Ultrapower Axiom.
Goldberg, Gabriel.

The Ultrapower Axiom. - 1 online resource (423 pages)

Source: Dissertations Abstracts International, Volume: 82-05, Section: B.

Thesis (Ph.D.)--Harvard University, 2019.

Includes bibliographical references

The inner model problem for supercompact cardinals, one of the central open problems in modern set theory, asks whether there is a canonical model of set theory with a supercompact cardinal. The problem is closely related to the more precise question of the equiconsistency of strongly compact cardinals and supercompact cardinals. This dissertation approaches these two problems abstractly by introducing a principle called the Ultrapower Axiom which is expected to hold in all known canonical models of set theory. By investigating the consequences of the Ultrapower Axiom under the hypothesis that there is a supercompact cardinal, we provide evidence that the inner model problem can be solved. Moreover, we establish that under the Ultrapower Axiom, strong compactness and supercompactness are essentially equivalent.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798684610455Subjects--Topical Terms:

527692
Mathematics.
Subjects--Index Terms:

Supercompact cardinalIndex Terms--Genre/Form:

554714
Electronic books.

The Ultrapower Axiom.
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500 $a Source: Dissertations Abstracts International, Volume: 82-05, Section: B.
500 $a Advisor: Woodin, W. Hugh.
502 $a Thesis (Ph.D.)--Harvard University, 2019.
504 $a Includes bibliographical references
520 $a The inner model problem for supercompact cardinals, one of the central open problems in modern set theory, asks whether there is a canonical model of set theory with a supercompact cardinal. The problem is closely related to the more precise question of the equiconsistency of strongly compact cardinals and supercompact cardinals. This dissertation approaches these two problems abstractly by introducing a principle called the Ultrapower Axiom which is expected to hold in all known canonical models of set theory. By investigating the consequences of the Ultrapower Axiom under the hypothesis that there is a supercompact cardinal, we provide evidence that the inner model problem can be solved. Moreover, we establish that under the Ultrapower Axiom, strong compactness and supercompactness are essentially equivalent.
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538 $a Mode of access: World Wide Web
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653 $a Supercompact cardinal
653 $a Ultrafilter
653 $a Ketonen order
653 $a Mitchell order
653 $a Rudin-Frolik order
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