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Principe de réflexion MRP, propriétés d'arbres et grands cardinaux

Abstract : The object of this thesis is to study the relashionships between the reflection principle MRP introduced by Moore, the generalized tree properties ITP and ISP introduced by Weiß, and the square properties introduced by Jensen and extended by Schimmerling. The main result is that MRP+MA implies ITP(λ, ω2) for all cardinals λ ≥ ω2. Consequently, all known methods for proving the consistency of MRP+MA require at least a supercompact cardinal. MRP alone is not enough to prove that result, and we give a proof that MRPdoes not imply the weakest tree property, TP(ω2, ω2). Furthermore, MRP + MA does not imply the stronger tree property ISP(ω2, ω2). In addition, we study the relationship between MRP and some weak versions of the square principle. We show that MRP implies the failure of square(λ, ω), and MRP + MA implies the failure of square(λ, ω1) for all λ ≥ ω2.
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https://tel.archives-ouvertes.fr/tel-00740730
Contributor : Rémi Strullu <>
Submitted on : Wednesday, October 10, 2012 - 5:42:16 PM
Last modification on : Saturday, April 11, 2020 - 1:51:22 AM
Long-term archiving on: : Friday, January 11, 2013 - 3:42:40 AM

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  • HAL Id : tel-00740730, version 1

Citation

Rémi Strullu. Principe de réflexion MRP, propriétés d'arbres et grands cardinaux. Logique [math.LO]. Université Paris-Diderot - Paris VII, 2012. Français. ⟨tel-00740730⟩

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