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  1. Aronszajn trees on ℵ2 and ℵ3.Uri Abraham - 1983 - Annals of Mathematical Logic 24 (3):213-230.
    Assuming the existence of a supercompact cardinal and a weakly compact cardinal above it, we provide a generic extension where there are no Aronszajn trees of height ω 2 or ω 3 . On the other hand we show that some large cardinal assumptions are necessary for such a consistency result.
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  • Strong tree properties for two successive cardinals.Laura Fontanella - 2012 - Archive for Mathematical Logic 51 (5-6):601-620.
    An inaccessible cardinal κ is supercompact when (κ, λ)-ITP holds for all λ ≥ κ. We prove that if there is a model of ZFC with two supercompact cardinals, then there is a model of ZFC where simultaneously \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(\aleph_2, \mu)}$$\end{document} -ITP and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(\aleph_3, \mu')}$$\end{document} -ITP hold, for all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mu\geq \aleph_2}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} (...)
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  • Some combinatorial problems concerning uncountable cardinals.Thomas J. Jech - 1973 - Annals of Mathematical Logic 5 (3):165.
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  • Set Theory. An Introduction to Independence Proofs.James E. Baumgartner & Kenneth Kunen - 1986 - Journal of Symbolic Logic 51 (2):462.
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  • Guessing models and generalized Laver diamond.Matteo Viale - 2012 - Annals of Pure and Applied Logic 163 (11):1660-1678.
    We analyze the notion of guessing model, a way to assign combinatorial properties to arbitrary regular cardinals. Guessing models can be used, in combination with inaccessibility, to characterize various large cardinal axioms, ranging from supercompactness to rank-to-rank embeddings. The majority of these large cardinal properties can be defined in terms of suitable elementary embeddings j:Vγ→Vλ. One key observation is that such embeddings are uniquely determined by the image structures j[Vγ]≺Vλ. These structures will be the prototypes guessing models. We shall show, (...)
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  • Aronszajn trees and the independence of the transfer property.William Mitchell - 1972 - Annals of Mathematical Logic 5 (1):21.
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  • On the Hamkins approximation property.William J. Mitchell - 2006 - Annals of Pure and Applied Logic 144 (1-3):126-129.
    We give a short proof of a lemma which generalizes both the main lemma from the original construction in the author’s thesis of a model with no ω2-Aronszajn trees, and also the “Key Lemma” in Hamkins’ gap forcing theorems. The new lemma directly yields Hamkins’ newer lemma stating that certain forcing notions have the approximation property.
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  • (1 other version)[Omnibus Review].Akihiro Kanamori - 1981 - Journal of Symbolic Logic 46 (4):864-866.
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  • On the notion of Guessing model.Matteo Viale - forthcoming - Annals of Pure and Applied Logic.
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