Acta Mathematica Hungarica
Volume/Issue:
Volume 137: Issue 4
The ultrafilter number for singular cardinals
Authors:
Shimon GartiInstitute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel

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Saharon ShelahInstitute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
Department of Mathematics, Rutgers University, New Brunswick NJ 08854, USA

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Pages:
296–301
Online Publication Date:
21 Jun 2012
Publication Date:
01 Dec 2012
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10474-012-0245-0
Keywords:
ultrafilter number; pcf theory; large cardinal; 03E05; 03E55
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Abstract

We prove the consistency of a singular cardinal λ with small value of the ultrafilter number , and arbitrarily large value of 2λ.

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  • [3] Burke, M. R. Magidor, M. 1990 Shelah's pcf theory and its applications Ann. Pure Appl. Logic 50 207–254 . MR 1086455 (92f:03053).

  • [4] Garti, S. and Shelah, S., A strong polarized relation, The Journal of Symbolic Logic (accepted).

  • [5] Gitik, M. 2010 Prikry-type forcings Handbook of Set Theory. Vols. 1, 2, 3 Springer Dordrecht 1351–1447 . MR 2768695.

  • [6] Shelah, S. 1994 Cardinal Arithmetic Oxford Logic Guides 29 The Clarendon Press Oxford University Press New York Oxford Science Publications. MR 1318912 (96e:03001).

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  • [7] Shelah, S. 2011 The character spectrum of β(ℕ) Topology Appl. 158 2535–2555 .

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Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1950
Volumes
per Year		 3
Issues
per Year		 6
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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