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December 2011 MRP, tree properties and square principles
Remi Strullu
J. Symbolic Logic 76(4): 1441-1452 (December 2011). DOI: 10.2178/jsl/1318338859

Abstract

We show that MRP+MA implies that ITP(λ,ω2) holds for all cardinal λ ≥ ω2. This generalizes a result by Weiß who showed that PFA implies that ITP(λ, ω2) holds for all cardinal λ ≥ ω2. Consequently any of the known methods to prove MRP+MA consistent relative to some large cardinal hypothesis requires the existence of a strongly compact cardinal. Moreover if one wants to force MRP+MA with a proper forcing, it requires at least a supercompact cardinal. We also study the relationship between MRP and some weak versions of square. We show that MRP implies the failure of □(λ,ω) for all λ≥ ω2 and we give a direct proof that MRP+MA implies the failure of □(λ,ω1) for all λ≥ω2.

Citation

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Remi Strullu. "MRP, tree properties and square principles." J. Symbolic Logic 76 (4) 1441 - 1452, December 2011. https://doi.org/10.2178/jsl/1318338859

Information

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

zbMATH: 1250.03100
MathSciNet: MR2895405
Digital Object Identifier: 10.2178/jsl/1318338859

Subjects:
Primary: 03E35 , 03E50 , 03E55 , 03E57

Keywords: consistency results , ITP , MRP , square sequence , strongly compact cardinal

Rights: Copyright © 2011 Association for Symbolic Logic

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Vol.76 • No. 4 • December 2011
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