Abstract

We prove some results in set theory as applied to general topology and model theory. In particular, we study ℵ1-collectionwise Hausdorff, Chang Conjecture for logics with Malitz-Magidor quantifiers and monadic logic of the real line by odd/even Cantor sets.

Highlights

  • The normal Moore space problem has been a major theme in general topology, see the recent survey Dow-Tall [9]

  • In [2] we prove the undecidability of the monadic theory of R, assuming CH, or the weaker Baire-like hypothesis that R is not the union of fewer than continuum sets of first category sets

  • Let P vary on Cantors and note that we can repeat the proof of [2] with small adaptation (and prove T is undecidable)

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Summary

Introduction

Earlier [2] proved this (i.e., the result on the monadic logic) assuming CH or at least a consequence of it. Have results related to Section 3; in particular it was conjectured there (in Remark 2.15) that there are two non-principal ultrafilters of ω with no common lower bound in the Rudin Keisler order; a conjecure which had been refuted in [4]. The author would like to thank Shai Ben David for stimulating discussions on part §3. We thank the referee for his help, well beyond than the call of duty

A Note in General Topology If
A Remark on the Monadic Theory of Order

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