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

Fundamenta Mathematicae (1998)

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

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topShelah, 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

top- [EHR] P. Erdős, A. Hajnal and R. Rado, Partition relations for cardinal numbers, Acta Math. Acad. Sci. Hungar. 16 (1965), 93-196. Zbl0158.26603
- [BH] J. Baumgartner and A. Hajnal, Polarized partition relations, preprint, 1995.
- [J] T. Jech, Set Theory, Academic Press, New York, 1978.
- [Sh:g] S. Shelah, Cardinal Arithmetic, Oxford Logic Guides 29, Oxford Univ. Press, 1994.
- [Sh 430] S. Shelah, Further cardinal arithmetic, Israel J. Math. 95 (1996), 61-114. Zbl0864.03032
- [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
- [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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