13 found
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  1.  33
    Simultaneous Stationary Reflection and Square Sequences.Yair Hayut & Chris Lambie-Hanson - 2017 - Journal of Mathematical Logic 17 (2):1750010.
    We investigate the relationship between weak square principles and simultaneous reflection of stationary sets.
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  2.  28
    Aronszajn Trees, Square Principles, and Stationary Reflection.Chris Lambie-Hanson - 2017 - Mathematical Logic Quarterly 63 (3-4):265-281.
    We investigate questions involving Aronszajn trees, square principles, and stationary reflection. We first consider two strengthenings of math formula introduced by Brodsky and Rinot for the purpose of constructing κ-Souslin trees. Answering a question of Rinot, we prove that the weaker of these strengthenings is compatible with stationary reflection at κ but the stronger is not. We then prove that, if μ is a singular cardinal, math formula implies the existence of a special math formula-tree with a cf-ascent path, thus (...)
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  3.  6
    Knaster and Friends II: The C-Sequence Number.Chris Lambie-Hanson & Assaf Rinot - 2020 - Journal of Mathematical Logic 21 (1):2150002.
    Motivated by a characterization of weakly compact cardinals due to Todorcevic, we introduce a new cardinal characteristic, the C-sequence number, which can be seen as a measure of the compactness of a regular uncountable cardinal. We prove a number of ZFC and independence results about the C-sequence number and its relationship with large cardinals, stationary reflection, and square principles. We then introduce and study the more general C-sequence spectrum and uncover some tight connections between the C-sequence spectrum and the strong (...)
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  4.  8
    Squares, Ascent Paths, and Chain Conditions.Chris Lambie-Hanson & Philipp Lücke - 2018 - Journal of Symbolic Logic 83 (4):1512-1538.
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  5.  18
    Squares and Covering Matrices.Chris Lambie-Hanson - 2014 - Annals of Pure and Applied Logic 165 (2):673-694.
    Viale introduced covering matrices in his proof that SCH follows from PFA. In the course of the proof and subsequent work with Sharon, he isolated two reflection principles, CP and S, which, under certain circumstances, are satisfied by all covering matrices of a certain shape. Using square sequences, we construct covering matrices for which CP and S fail. This leads naturally to an investigation of square principles intermediate between □κ and □ for a regular cardinal κ. We provide a detailed (...)
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  6.  9
    Diagonal Supercompact Radin Forcing.Omer Ben-Neria, Chris Lambie-Hanson & Spencer Unger - 2020 - Annals of Pure and Applied Logic 171 (10):102828.
    Motivated by the goal of constructing a model in which there are no κ-Aronszajn trees for any regular $k>\aleph_1$, we produce a model with many singular cardinals where both the singular cardinals hypothesis and weak square fail.
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  7.  7
    Separating Diagonal Stationary Reflection Principles.Gunter Fuchs & Chris Lambie-Hanson - 2021 - Journal of Symbolic Logic 86 (1):262-292.
    We introduce three families of diagonal reflection principles for matrices of stationary sets of ordinals. We analyze both their relationships among themselves and their relationships with other known principles of simultaneous stationary reflection, the strong reflection principle, and the existence of square sequences.
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  8.  8
    The Hanf Number for Amalgamation of Coloring Classes.Alexei Kolesnikov & Chris Lambie-Hanson - 2016 - Journal of Symbolic Logic 81 (2):570-583.
  9.  10
    Good and Bad Points in Scales.Chris Lambie-Hanson - 2014 - Archive for Mathematical Logic 53 (7-8):749-777.
    We address three questions raised by Cummings and Foreman regarding a model of Gitik and Sharon. We first analyze the PCF-theoretic structure of the Gitik–Sharon model, determining the extent of good and bad scales. We then classify the bad points of the bad scales existing in both the Gitik–Sharon model and other models containing bad scales. Finally, we investigate the ideal of subsets of singular cardinals of countable cofinality carrying good scales.
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  10.  17
    Bounded Stationary Reflection II.Chris Lambie-Hanson - 2017 - Annals of Pure and Applied Logic 168 (1):50-71.
  11.  3
    Simultaneously Vanishing Higher Derived Limits Without Large Cardinals.Jeffrey Bergfalk, Michael Hrusak & Chris Lambie-Hanson - forthcoming - Journal of Mathematical Logic.
  12.  8
    Forcing a □(Κ)-Like Principle to Hold at a Weakly Compact Cardinal.Brent Cody, Victoria Gitman & Chris Lambie-Hanson - 2021 - Annals of Pure and Applied Logic 172 (7):102960.
  13. Knaster and Friends III: Subadditive Colorings.Chris Lambie-Hanson & Assaf Rinot - forthcoming - Journal of Symbolic Logic:1-48.
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