## Notre Dame Journal of Formal Logic

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

Claribet Piña

#### 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
Accepted: 4 March 2016
First available in Project Euclid: 26 June 2018

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
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