Journal of Symbolic Logic

Bounds for covering numbers

Andreas Liu
Source: J. Symbolic Logic Volume 71, Issue 4 (2006), 1303-1310.

Abstract

Let λ be a singular cardinal of uncountable cofinality ν. Under various assumptions about the sizes of covering families for cardinals below λ, we prove upper bounds for the covering number cov(λ,λ,ν⁺,2). This covering number is closely related to the cofinality of the partial order ([λ]ν,⊆).

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.jsl/1164060456
Digital Object Identifier: doi:10.2178/jsl/1164060456
Mathematical Reviews number (MathSciNet): MR2275860
Zentralblatt MATH identifier: 1109.03044

References

P. Erdős, A. Hajnal, A. Maté, and R. Rado, Combinatorial set theory: Partition relations for cardinals, Studies in Logic and the Foundations of Mathematics, vol. 106, North Holland, Amsterdam, 1984.
Mathematical Reviews (MathSciNet): MR795592
M. Gitik, Introduction to Prikry type forcing notions, to appear in Handbook of Set Theory.
A. Liu, Reflecting pictures in cardinal arithmetic, Annals of Pure and Applied Logic, vol. 140 (2006), pp. 120--127.
Mathematical Reviews (MathSciNet): MR2224054
Digital Object Identifier: doi:10.1016/j.apal.2005.09.007
Zentralblatt MATH: 1106.03043
S. Shelah, Advances in cardinal arithmetic, Finite and infinite combinatorics in sets and logic, 1993, pp. 355--383.
Mathematical Reviews (MathSciNet): MR1261217
Zentralblatt MATH: 0844.03028
--------, Cardinal arithmetic, Oxford Logic Guides, vol. 29, Oxford University Press, Oxford, 1994.
Mathematical Reviews (MathSciNet): MR1318912
Zentralblatt MATH: 0848.03025
--------, Applications of pcf theory, Journal of Symbolic Logic, vol. 65 (2000), pp. 1624--1674.
Mathematical Reviews (MathSciNet): MR1812172
Digital Object Identifier: doi:10.2307/2695067
Project Euclid: euclid.jsl/1183746255
Zentralblatt MATH: 0981.03048
--------, The generalized continuum hypothesis revisited, Israel Journal of Mathematics, vol. 116 (2000), pp. 285--321.
Mathematical Reviews (MathSciNet): MR1759410
Digital Object Identifier: doi:10.1007/BF02773223
Zentralblatt MATH: 0955.03054
--------, More on the revised GCH and the black box, Annals of Pure and Applied Logic, vol. 140 (2006), pp. 133--160.
Mathematical Reviews (MathSciNet): MR2224056
Digital Object Identifier: doi:10.1016/j.apal.2005.09.013
Zentralblatt MATH: 1100.03043

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Journal of Symbolic Logic

Journal of Symbolic Logic

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