First countable, countably compact spaces and the continuum hypothesis
Continuum Hypothesis, Iterations, Pre-images of ω 1, Proper forcing
Transactions of the American Mathematical Society
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
DOI of published version
Eisworth, Todd and Nyikos, Peter, "First countable, countably compact spaces and the continuum hypothesis" (2005). Faculty Publications. 2908.