Translator Disclaimer
September 2008 On a result of Szemerédi
Albin L. Jones
J. Symbolic Logic 73(3): 953-956 (September 2008). DOI: 10.2178/jsl/1230396758

Abstract

We provide a short proof that if $\kappa$ is a regular cardinal with $\kappa \leq \mathfrak{c}$, then $\left(\begin{matrix} \kappa \\ \omega \end{matrix}\right) \rightarrow \left(\begin{matrix} \kappa~~~\alpha \\ \omega~~~\omega \end{matrix} \right)^{1,1}$ for any ordinal $\alpha$ < min {$\mathfrak{p},\kappa$}. In particular, $\left(\begin {matrix} \mathfrak{p} \\ \omega \end{matrix}\right) \rightarrow \left(\begin{matrix} \mathfrak{p}~~~\alpha \\ \omega~~~\omega \end{matrix}\right)^{1,1}$ for any ordinal $\alpha < \mathfrak{p}$. This generalizes an unpublished result of E. Szemerédi that Martin’s axiom implies that $\left(\begin{matrix} \mathfrak{c} \\ \omega \end{matrix}\right) \rightarrow \left(\begin{matrix} \mathfrak{c}~~~\kappa \\ \omega~~~\omega \end{matrix}\right)^{1,1}$. for any cardinal $\kappa$ with $\kappa < \mathfrak{c}$.

Citation

Download Citation

Albin L. Jones. "On a result of Szemerédi." J. Symbolic Logic 73 (3) 953 - 956, September 2008. https://doi.org/10.2178/jsl/1230396758

Information

Published: September 2008
First available in Project Euclid: 27 December 2008

zbMATH: 1163.03024
MathSciNet: MR2444279
Digital Object Identifier: 10.2178/jsl/1230396758

Subjects:
Primary: 03E05, 05D10
Secondary: 05A18

Rights: Copyright © 2008 Association for Symbolic Logic

JOURNAL ARTICLE
4 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.73 • No. 3 • September 2008
Back to Top