## Notre Dame Journal of Formal Logic

- Notre Dame J. Formal Logic
- Volume 59, Number 3 (2018), 387-403.

### A Partition Theorem of ${\omega}^{{\omega}^{\alpha}}$

#### Abstract

We consider finite partitions of the closure $\overline{\mathcal{F}}$ of an ${\omega}^{\alpha}$-uniform barrier $\mathcal{F}$. For each partition, we get a homogeneous set having both the same combinatorial and topological structure as $\overline{\mathcal{F}}$, seen as a subspace of the Cantor space ${2}^{\mathbb{N}}$.

#### Article information

**Source**

Notre Dame J. Formal Logic, Volume 59, Number 3 (2018), 387-403.

**Dates**

Received: 2 April 2015

Accepted: 4 March 2016

First available in Project Euclid: 26 June 2018

**Permanent link to this document**

https://projecteuclid.org/euclid.ndjfl/1529978581

**Digital Object Identifier**

doi:10.1215/00294527-2018-0001

**Mathematical Reviews number (MathSciNet)**

MR3832088

**Zentralblatt MATH identifier**

06939327

**Subjects**

Primary: 03E02: Partition relations

Secondary: 05D10: Ramsey theory [See also 05C55]

**Keywords**

partition of topological spaces uniform barriers U-trees

#### Citation

Piña, Claribet. A Partition Theorem of $\omega^{\omega^{\alpha}}$. Notre Dame J. Formal Logic 59 (2018), no. 3, 387--403. doi:10.1215/00294527-2018-0001. https://projecteuclid.org/euclid.ndjfl/1529978581