A polarized partition relation and failure of GCH at singular strong limit

Saharon Shelah

Fundamenta Mathematicae (1998)

  • Volume: 155, Issue: 2, page 153-160
  • ISSN: 0016-2736

Abstract

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The main result is that for λ strong limit singular failing the continuum hypothesis (i.e. 2 λ > λ + ), a polarized partition theorem holds.

How to cite

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Shelah, Saharon. "A polarized partition relation and failure of GCH at singular strong limit." Fundamenta Mathematicae 155.2 (1998): 153-160. <http://eudml.org/doc/212248>.

@article{Shelah1998,
abstract = {The main result is that for λ strong limit singular failing the continuum hypothesis (i.e. $2^\{λ\} > λ^\{+\}$), a polarized partition theorem holds.},
author = {Shelah, Saharon},
journal = {Fundamenta Mathematicae},
keywords = {GCH; polarized partition relation; singular cardinal; pcf theory},
language = {eng},
number = {2},
pages = {153-160},
title = {A polarized partition relation and failure of GCH at singular strong limit},
url = {http://eudml.org/doc/212248},
volume = {155},
year = {1998},
}

TY - JOUR
AU - Shelah, Saharon
TI - A polarized partition relation and failure of GCH at singular strong limit
JO - Fundamenta Mathematicae
PY - 1998
VL - 155
IS - 2
SP - 153
EP - 160
AB - The main result is that for λ strong limit singular failing the continuum hypothesis (i.e. $2^{λ} > λ^{+}$), a polarized partition theorem holds.
LA - eng
KW - GCH; polarized partition relation; singular cardinal; pcf theory
UR - http://eudml.org/doc/212248
ER -

References

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  1. [EHR] P. Erdős, A. Hajnal and R. Rado, Partition relations for cardinal numbers, Acta Math. Acad. Sci. Hungar. 16 (1965), 93-196. Zbl0158.26603
  2. [BH] J. Baumgartner and A. Hajnal, Polarized partition relations, preprint, 1995. 
  3. [J] T. Jech, Set Theory, Academic Press, New York, 1978. 
  4. [Sh:g] S. Shelah, Cardinal Arithmetic, Oxford Logic Guides 29, Oxford Univ. Press, 1994. 
  5. [Sh 430] S. Shelah, Further cardinal arithmetic, Israel J. Math. 95 (1996), 61-114. Zbl0864.03032
  6. [Sh 420] S. Shelah, Advances in cardinal arithmetic, in: Finite and Infinite Combinatorics in Sets and Logic, N. W. Sauer et al. (eds.), Kluwer Acad. Publ., 1993, 355-383. Zbl0844.03028
  7. [Sh 108] S. Shelah, On successors of singular cardinals, in: Logic Colloquium '78 (Mons, 1978), Stud. Logic Found. Math. 97, North-Holland, Amsterdam, 1979, 357-380. 

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