| Title:
|
Spectra of uniformity (English) |
| Author:
|
Hayut, Yair |
| Author:
|
Karagila, Asaf |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
60 |
| Issue:
|
2 |
| Year:
|
2019 |
| Pages:
|
285-298 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
uniform ultrafilter |
| Keyword:
|
axiom of choice |
| Keyword:
|
measurable cardinal |
| Keyword:
|
strongly compact cardinal |
| MSC:
|
03E25 |
| MSC:
|
03E35 |
| MSC:
|
03E55 |
| idZBL:
|
Zbl 07144894 |
| idMR:
|
MR3982473 |
| DOI:
|
10.14712/1213-7243.2019.008 |
| . |
| Date available:
|
2019-08-05T09:53:24Z |
| Last updated:
|
2021-07-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147812 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Feferman S.: Some applications of the notions of forcing and generic sets.Fund. Math. 56 (1964/1965), 325–345. MR 0176925, 10.4064/fm-56-3-325-345 |
| Reference:
|
[4] Herrlich H., Howard P., Keremedis K.: On preimages of ultrafilters in $\mathsf{ZF}$.Comment. Math. Univ. Carolin. 57 (2016), no. 2, 241–252. MR 3513447 |
| Reference:
|
[5] Jech T.: Set Theory.Springer Monographs in Mathematics, Springer, Berlin, 2003. Zbl 1007.03002, MR 1940513 |
| Reference:
|
[6] Karagila A.: Embedding orders into the cardinals with $\mathsf{DC}_\kappa$.Fund. Math. 226 (2014), no. 2, 143–156. MR 3224118, 10.4064/fm226-2-4 |
| Reference:
|
[7] Solovay R. M.: A model of set-theory in which every set of reals is Lebesgue measurable.Ann. of Math. (2) 92 (1970), 1–56. Zbl 0207.00905, MR 0265151, 10.2307/1970696 |
| Reference:
|
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| . |
