Singular cardinals and strong extenders
Arthur Apter; James Cummings; Joel Hamkins
Open Mathematics (2013)
- Volume: 11, Issue: 9, page 1628-1634
- ISSN: 2391-5455
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topArthur Apter, James Cummings, and Joel Hamkins. "Singular cardinals and strong extenders." Open Mathematics 11.9 (2013): 1628-1634. <http://eudml.org/doc/269814>.
@article{ArthurApter2013,
abstract = {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).},
author = {Arthur Apter, James Cummings, Joel Hamkins},
journal = {Open Mathematics},
keywords = {Strong cardinal; Extender; Inner model; Singular cardinal; strong cardinal; extender; inner model; singular cardinal},
language = {eng},
number = {9},
pages = {1628-1634},
title = {Singular cardinals and strong extenders},
url = {http://eudml.org/doc/269814},
volume = {11},
year = {2013},
}
TY - JOUR
AU - Arthur Apter
AU - James Cummings
AU - Joel Hamkins
TI - Singular cardinals and strong extenders
JO - Open Mathematics
PY - 2013
VL - 11
IS - 9
SP - 1628
EP - 1634
AB - 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).
LA - eng
KW - Strong cardinal; Extender; Inner model; Singular cardinal; strong cardinal; extender; inner model; singular cardinal
UR - http://eudml.org/doc/269814
ER -
References
top- [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 Zbl1145.03032
- [3] Gitik M., personal communication, 2012
- [4] Kanamori A., The Higher Infinite, Perspect. Math. Logic, Springer, Berlin, 1994 Zbl0813.03034
- [5] Mitchell W.J., Sets constructible from sequences of ultrafilters, J. Symbolic Logic, 1974, 39, 57–66 http://dx.doi.org/10.2307/2272343 Zbl0295.02040
- [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
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