Translator Disclaimer
December 2011 Forcings constructed along morasses
Bernhard Irrgang
J. Symbolic Logic 76(4): 1097-1125 (December 2011). DOI: 10.2178/jsl/1318338841

Abstract

We further develop a previously introduced method of constructing forcing notions with the help of morasses. There are two new results: (1) If there is a simplified (ω1,1)-morass, then there exists a ccc forcing of size ω1 that adds an ω2-Suslin tree. (2) If there is a simplified (ω1,2)-morass, then there exists a ccc forcing of size ω1 that adds a 0-dimensional Hausdorff topology τ on ω3 which has spread s(τ)=ω1. While (2) is the main result of the paper, (1) is only an improvement of a previous result, which is based on a simple observation. Both forcings preserve GCH. To show that the method can be changed to produce models where CH fails, we give an alternative construction of Koszmider's model in which there is a chain 〈 Xα | α < ω2〉 such that Xα ⊆ ω1, Xβ -Xα is finite and Xα-Xβ has size ω1 for all β < α <ω2.

Citation

Download Citation

Bernhard Irrgang. "Forcings constructed along morasses." J. Symbolic Logic 76 (4) 1097 - 1125, December 2011. https://doi.org/10.2178/jsl/1318338841

Information

Published: December 2011
First available in Project Euclid: 11 October 2011

zbMATH: 1250.03096
MathSciNet: MR2895388
Digital Object Identifier: 10.2178/jsl/1318338841

Rights: Copyright © 2011 Association for Symbolic Logic

JOURNAL ARTICLE
29 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.76 • No. 4 • December 2011
Back to Top