A new Easton theorem for supercompactness and level by level equivalence

• Autorzy: Apter A. W.

Identyfikatory

DOI

10.4064/ba8080-6-2017

• Języki publikacji: EN

Abstrakty

EN

We establish a new Easton theorem for the least supercompact cardinal κ that is consistent with the level by level equivalence between strong compactness and supercompactness. This theorem is true in any model of ZFC containing at least one supercompact cardinal, regardless if level by level equivalence holds. Unlike previous Easton theorems for supercompactness, there are no limits on the Easton functions F used, other than the usual constraints given by Easton’s theorem and the fact that if δ < κ is regular, then F(δ) < κ 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.

Słowa kluczowe

EN

supercompact cardinal; strongly compact cardinal; strong cardinal; level by level equivalence; strong compactness; upercompactness; Easton theorem

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2017
• Tom: Vol. 65, no. 1
• Strony: 1--10
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Apter A. W.

• Department of Mathematics, Baruch College of CUNY, New York, NY, 10010, U.S.A.
• The CUNY Graduate Center, Mathematics, 365 Fifth Avenue, New York, NY, 10016, USA

Bibliografia

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• [10] A. Lévy and R. Solovay, Measurable cardinals and the continuum hypothesis, Israel J. Math. 5 (1967), 234–248.
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Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).