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Souslin forcing

Published online by Cambridge University Press:  12 March 2014

Jaime I. Ihoda  and
Saharon Shelah
Jaime I. Ihoda
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720
Saharon Shelah
Affiliation:
Universidad Católica De Chile, Santiago, Chile Institute of Mathematics, The Hebrew University, Jerusalem, Israel Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
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Abstract

We define the notion of Souslin forcing, and we prove that some properties are preserved under iteration. We define a weaker form of Martin's axiom, namely , and using the results on Souslin forcing we show that is consistent with the existence of a Souslin tree and with the splitting number s = ℵ1. We prove that proves the additivity of measure. Also we introduce the notion of proper Souslin forcing, and we prove that this property is preserved under countable support iterated forcing. We use these results to show that ZFC + there is an inaccessible cardinal is equiconsistent with ZFC + the Borel conjecture + -measurability.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 53 , Issue 4 , December 1988 , pp. 1188 - 1207
Copyright
Copyright © Association for Symbolic Logic 1988

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