Real Analysis Exchange

Covering Numbers Associated with Trees Branching into a Countably Generated Set of Possibilities

Saharon Shelah

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Abstract

One can think of the dominating number as the covering number for the ideal on the $\omega$-branching tree generated by finite branching subtrees. This paper is concerned with generalizations of this when "finite" is replaced by some other concept. A key example is obtained by thinking of the branching as being into the integers --- both positive and negative --- and replacing "finite" by "bounded either above or below". This notion was motivated by considerations related to decomposing functions of low Baire class into continuous functions.

Article information

Source
Real Anal. Exchange, Volume 24, Number 1 (1998), 205-214.

Dates
First available in Project Euclid: 23 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.rae/1300906023

Mathematical Reviews number (MathSciNet)
MR1691746

Zentralblatt MATH identifier
0938.03074

Subjects
Primary: 03E35: Consistency and independence results 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]

Keywords
covering numbers

Citation

Shelah, Saharon. Covering Numbers Associated with Trees Branching into a Countably Generated Set of Possibilities. Real Anal. Exchange 24 (1998), no. 1, 205--214. https://projecteuclid.org/euclid.rae/1300906023


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References

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