## Real Analysis Exchange

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

Saharon Shelah

#### 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

https://projecteuclid.org/euclid.rae/1300906023

Mathematical Reviews number (MathSciNet)
MR1691746

Zentralblatt MATH identifier
0938.03074

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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