Open Access
January, 2011 Eventually different functions and inaccessible cardinals
Jörg BRENDLE, Benedikt LÖWE
J. Math. Soc. Japan 63(1): 137-151 (January, 2011). DOI: 10.2969/jmsj/06310137


In this paper, we are considering the Baire property of the eventually different topology as a regularity property for sets of reals and investigate the logical strength of the statements "Every $\Delta_2^1$ set has the Baire property in the eventually different topology" and "Every $\Sigma_2^1$ set has the Baire property in the eventually different topology". The latter statement turns out to be equivalent to "$\omega_1$ is inaccessible by reals".


Download Citation

Jörg BRENDLE. Benedikt LÖWE. "Eventually different functions and inaccessible cardinals." J. Math. Soc. Japan 63 (1) 137 - 151, January, 2011.


Published: January, 2011
First available in Project Euclid: 27 January 2011

zbMATH: 1215.03059
MathSciNet: MR2752434
Digital Object Identifier: 10.2969/jmsj/06310137

Primary: 03E15
Secondary: 03E40 , 03E55

Keywords: eventually different forcing , Hechler forcing , regularity properties

Rights: Copyright © 2011 Mathematical Society of Japan

Vol.63 • No. 1 • January, 2011
Back to Top