Spectra of uniformity

Yair Hayut; Asaf Karagila

Commentationes Mathematicae Universitatis Carolinae (2019)

  • Volume: 60, Issue: 2, page 285-298
  • ISSN: 0010-2628

Abstract

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We study some limitations and possible occurrences of uniform ultrafilters on ordinals without the axiom of choice. We prove an Easton-like theorem about the possible spectrum of successors of regular cardinals which carry uniform ultrafilters; we also show that this spectrum is not necessarily closed.

How to cite

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Hayut, Yair, and Karagila, Asaf. "Spectra of uniformity." Commentationes Mathematicae Universitatis Carolinae 60.2 (2019): 285-298. <http://eudml.org/doc/294641>.

@article{Hayut2019,
abstract = {We study some limitations and possible occurrences of uniform ultrafilters on ordinals without the axiom of choice. We prove an Easton-like theorem about the possible spectrum of successors of regular cardinals which carry uniform ultrafilters; we also show that this spectrum is not necessarily closed.},
author = {Hayut, Yair, Karagila, Asaf},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {uniform ultrafilter; axiom of choice; measurable cardinal; strongly compact cardinal},
language = {eng},
number = {2},
pages = {285-298},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Spectra of uniformity},
url = {http://eudml.org/doc/294641},
volume = {60},
year = {2019},
}

TY - JOUR
AU - Hayut, Yair
AU - Karagila, Asaf
TI - Spectra of uniformity
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2019
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 60
IS - 2
SP - 285
EP - 298
AB - We study some limitations and possible occurrences of uniform ultrafilters on ordinals without the axiom of choice. We prove an Easton-like theorem about the possible spectrum of successors of regular cardinals which carry uniform ultrafilters; we also show that this spectrum is not necessarily closed.
LA - eng
KW - uniform ultrafilter; axiom of choice; measurable cardinal; strongly compact cardinal
UR - http://eudml.org/doc/294641
ER -

References

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  2. Blass A., A model without ultrafilters, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (1977), no. 4, 329–331. MR0476510
  3. Feferman S., 10.4064/fm-56-3-325-345, Fund. Math. 56 (1964/1965), 325–345. MR0176925DOI10.4064/fm-56-3-325-345
  4. Herrlich H., Howard P., Keremedis K., On preimages of ultrafilters in 𝖹𝖥 , Comment. Math. Univ. Carolin. 57 (2016), no. 2, 241–252. MR3513447
  5. Jech T., Set Theory, Springer Monographs in Mathematics, Springer, Berlin, 2003. Zbl1007.03002MR1940513
  6. Karagila A., 10.4064/fm226-2-4, Fund. Math. 226 (2014), no. 2, 143–156. MR3224118DOI10.4064/fm226-2-4
  7. Solovay R. M., 10.2307/1970696, Ann. of Math. (2) 92 (1970), 1–56. Zbl0207.00905MR0265151DOI10.2307/1970696
  8. Truss J., 10.1016/0003-4843(74)90015-1, Ann. Math. Logic 7 (1974), no. 2–3, 197–219. MR0369068DOI10.1016/0003-4843(74)90015-1

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