## Real Analysis Exchange

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

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

#### 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