Obtaining Woodin's cardinals

Philip D Welch

doi:10.1090/conm/690/13867

Obtaining Woodin's cardinals

Philip D Welch^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter in a book

6 Citations (Scopus)

487 Downloads (Pure)

Abstract

Since the 1980’s work on Projective Determinacy and AD^L(R) the concept of Woodin cardinal has become to be seen as central in the theory of large cardinals and inner model theory. The use by Woodin himself of a background assumption in many arguments that the universe contains unboundedly many such cardinals again draws attention to the centrality of this concept.

As is well known the Reflection Principles dating to a more classicial era only provide large cardinals consistent with V = L, and not the wherewithal for such theorems on absoluteness under set forcing that Woodin has proven.

We discuss here a reflection principle derived from weak sub-compactness that implies the existence of a proper class of measurable Woodin cardinals - thus providing adequate background assumptions for many of Woodin’s absoluteness results in his work

Original language	English
Title of host publication	Foundations of Mathematics
Subtitle of host publication	Logic at Harvard: Essays in Honor of W. Hugh Woodin's 60th Birthday, March 27-29 2015, Harvard University, Cambridge, MA
Editors	Andres Eduardo Caicedo, James Cummings, Peter Koellner, Paul B Larson
Publisher	American Mathematical Society
Pages	161-176
Number of pages	16
ISBN (Electronic)	9781470440794
ISBN (Print)	9781470422561
DOIs	https://doi.org/10.1090/conm/690/13867
Publication status	Published - 30 May 2017

Publication series

Name	Contemporary Mathematics
Publisher	American Mathematical Society
Volume	690
ISSN (Print)	0271-4132
ISSN (Electronic)	1098-3627

Keywords

Reflection
Woodin cardinals

Access to Document

10.1090/conm/690/13867

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Welch, P. D. (2017). Obtaining Woodin's cardinals. In A. E. Caicedo, J. Cummings, P. Koellner, & P. B. Larson (Eds.), Foundations of Mathematics: Logic at Harvard: Essays in Honor of W. Hugh Woodin's 60th Birthday, March 27-29 2015, Harvard University, Cambridge, MA (pp. 161-176). (Contemporary Mathematics; Vol. 690). American Mathematical Society. https://doi.org/10.1090/conm/690/13867

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Welch, PD 2017, Obtaining Woodin's cardinals. in AE Caicedo, J Cummings, P Koellner & PB Larson (eds), Foundations of Mathematics: Logic at Harvard: Essays in Honor of W. Hugh Woodin's 60th Birthday, March 27-29 2015, Harvard University, Cambridge, MA. Contemporary Mathematics, vol. 690, American Mathematical Society, pp. 161-176. https://doi.org/10.1090/conm/690/13867

Obtaining Woodin's cardinals. / Welch, Philip D.
Foundations of Mathematics: Logic at Harvard: Essays in Honor of W. Hugh Woodin's 60th Birthday, March 27-29 2015, Harvard University, Cambridge, MA. ed. / Andres Eduardo Caicedo; James Cummings; Peter Koellner; Paul B Larson. American Mathematical Society, 2017. p. 161-176 (Contemporary Mathematics; Vol. 690).

Research output: Chapter in Book/Report/Conference proceeding › Chapter in a book

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Obtaining Woodin's cardinals

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Professor Philip D Welch

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Obtaining Woodin's cardinals

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Keywords

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Professor Philip D Welch

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