Singular cardinals and strong extenders
Arthur Apter ; James Cummings ; Joel Hamkins
Open Mathematics, Tome 11 (2013), p. 1628-1634 / Harvested from The Polish Digital Mathematics Library

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).

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:269814
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     author = {Arthur Apter and James Cummings and Joel Hamkins},
     title = {Singular cardinals and strong extenders},
     journal = {Open Mathematics},
     volume = {11},
     year = {2013},
     pages = {1628-1634},
     zbl = {1315.03088},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0265-1}
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Arthur Apter; James Cummings; Joel Hamkins. Singular cardinals and strong extenders. Open Mathematics, Tome 11 (2013) pp. 1628-1634. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0265-1/

[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 | Zbl 1145.03032

[3] Gitik M., personal communication, 2012

[4] Kanamori A., The Higher Infinite, Perspect. Math. Logic, Springer, Berlin, 1994 | Zbl 0813.03034

[5] Mitchell W.J., Sets constructible from sequences of ultrafilters, J. Symbolic Logic, 1974, 39, 57–66 http://dx.doi.org/10.2307/2272343 | Zbl 0295.02040

[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