Faculty Publications

Title

First countable, countably compact spaces and the continuum hypothesis

Document Type

Article

Keywords

Continuum Hypothesis, Iterations, Pre-images of ω 1, Proper forcing

Journal/Book/Conference Title

Transactions of the American Mathematical Society

Volume

357

Issue

11

First Page

4269

Last Page

4299

Abstract

We build a model of ZFC+CH in which every first countable, countably compact space is either compact or contains a homeomorphic copy of ω 1 with the order topology. The majority of the paper consists of developing forcing technology that allows us to conclude that our iteration adds no reals. Our results generalize Saharon Shelah's iteration theorems appearing in Chapters V and VIII of Proper and improper forcing (1998), as well as Eisworth and Roitman's (1999) iteration theorem. We close the paper with a ZFC example (constructed using Shelah's club-guessing sequences) that shows similar results do not hold for closed pre-images of ω 2. ©2005 American Mathematical Society.

Original Publication Date

11-1-2005

DOI of published version

10.1090/S0002-9947-05-04034-1

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