Forcing axioms and the continuum hypothesis

Aspero, David, Larson, Paul and Moore, Justin Tatch (2013) Forcing axioms and the continuum hypothesis. Acta Mathematica, 210 (1). pp. 1-29. ISSN 0001-5962

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Abstract

Woodin has demonstrated that, in the presence of large cardinals, there is a single model of ZFC which is maximal for ?-sentences over the structure (H(?), ?, NS), in the sense that its (H(?), ?, NS) satisfies every ?-sentence s for which (H(?), ?, NS) {true} s can be forced by set-forcing. In this paper we answer a question of Woodin by showing that there are two ?-sentences over the structure (H(?), ?, ?) which can each be forced to hold along with the continuum hypothesis, but whose conjunction implies,. In the process we establish that there are two preservation theorems for not introducing new real numbers by a countable support iterated forcing which cannot be subsumed into a single preservation theorem.

Item Type:	Article
Uncontrolled Keywords:	continuum hypothesis,iterated forcing,forcing axiom,martin's maximum,Π2 maximality,proper forcing axiom,03e35,03e50,03e57
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Logic (former - to 2024) Faculty of Science > Research Groups > Algebra, Logic & Number Theory
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	Pure Connector
Date Deposited:	01 Nov 2013 14:40
Last Modified:	07 Nov 2024 12:37
URI:	https://ueaeprints.uea.ac.uk/id/eprint/44056
DOI:	10.1007/s11511-013-0089-7

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