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Distinguishing types of gaps in (ω)/fin

Published online by Cambridge University Press:  12 March 2014

Teruyuki Yorioka
Affiliation:
Graduate School of Science and Technology, Kobe University, Rokkodai, Nada-Ku, Kobe 657-8501, Japan, E-mail: yorioka@kurt.scitec.kobe-u.ac.jp
Corresponding

Abstract

Supplementing the well known results of Kunen we show that Martin's Axiom is not sufficient to decide the existence of (ω 1, ϲ)-gaps when (ϲ, ϲ)-gaps exist, that is, it is consistent with ZFC that Martin's Axiom holds and there are (ϲ, ϲ)-gaps but no (ω 1, ϲ)-gaps.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2003

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