Singular cardinals and strong extenders

• Autorzy: Arthur Apter , James Cummings , Joel Hamkins
• Języki publikacji: EN

Abstrakty

EN

We investigate the circumstances under which there exist a singular cardinal µ and a short (κ,µ)-extender E witnessing “κ is µ-strong”, such that µ is singular in Ult(V, E).

Słowa kluczowe

EN

Strong cardinal; Extender; Inner model; Singular cardinal

Kategorie tematyczne

• 03E55: Large cardinals
• 03E45: Inner models, including constructibility, ordinal definability, and core models
• 03E35: Consistency and independence results

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 9
• Strony: 1628-1634

Daty

wydano

2013-09-01

online

2013-06-28

Twórcy

autor

Arthur Apter

autor

James Cummings

• Carnegie Mellon University

autor

Joel Hamkins

Bibliografia

• [1] Cody B., Some Results on Large Cardinals and the Continuum Function, PhD thesis, CUNY Graduate Center, New York, 2012
• [2] Friedman S.-D., Honzik R., Easton’s theorem and large cardinals, Ann. Pure Appl. Logic, 2008, 154(3), 191–208 http://dx.doi.org/10.1016/j.apal.2008.02.001
• [3] Gitik M., personal communication, 2012
• [4] Kanamori A., The Higher Infinite, Perspect. Math. Logic, Springer, Berlin, 1994
• [5] Mitchell W.J., Sets constructible from sequences of ultrafilters, J. Symbolic Logic, 1974, 39, 57–66 http://dx.doi.org/10.2307/2272343
• [6] Mitchell W., Hypermeasurable cardinals, In: Logic Colloquium’ 78, Mons, 1978, Stud. Logic Foundations Math., 97, North-Holland, Amsterdam-New York, 1979, 303–316 http://dx.doi.org/10.1016/S0049-237X(08)71631-8
• [7] Mitchell W.J., Beginning inner model theory, In: Handbook of Set Theory, Springer, Dordrecht, 2010, 1449–1495 http://dx.doi.org/10.1007/978-1-4020-5764-9_18

Identyfikatory

DOI

10.2478/s11533-013-0265-1