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An Easton theorem for level by level equivalence

✍ Scribed by Arthur W. Apter

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 130 KB
Volume: 51
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200510023

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✦ Synopsis

MSC (2000) 03E35, 03E55

We establish an Easton theorem for the least supercompact cardinal that is consistent with the level by level equivalence between strong compactness and supercompactness. In both our ground model and the model witnessing the conclusions of our theorem, there are no restrictions on the structure of the class of supercompact cardinals. We also briefly indicate how our methods of proof yield an Easton theorem that is consistent with the level by level equivalence between strong compactness and supercompactness in a universe with a restricted number of large cardinals. We conclude by posing some related open questions.

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