16 found
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  1.  44
    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.  22
    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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  3.  27
    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.  37
    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 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, implies the existence of a special ‐tree with a cf(μ)‐ascent path, thus answering a question of Lücke.
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  5.  20
    Squares, ascent paths, and chain conditions.Chris Lambie-Hanson & Philipp Lücke - 2018 - Journal of Symbolic Logic 83 (4):1512-1538.
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  6.  6
    Two-Cardinal Derived Topologies, Indescribability and Ramseyness.Brent Cody, Chris Lambie-Hanson & Jing Zhang - forthcoming - Journal of Symbolic Logic:1-29.
    We introduce a natural two-cardinal version of Bagaria’s sequence of derived topologies on ordinals. We prove that for our sequence of two-cardinal derived topologies, limit points of sets can be characterized in terms of a new iterated form of pairwise simultaneous reflection of certain kinds of stationary sets, the first few instances of which are often equivalent to notions related to strong stationarity, which has been studied previously in the context of strongly normal ideals. The non-discreteness of these two-cardinal derived (...)
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  7.  13
    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.
  8.  29
    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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  9.  19
    Simultaneously vanishing higher derived limits without large cardinals.Jeffrey Bergfalk, Michael Hrušák & Chris Lambie-Hanson - 2022 - Journal of Mathematical Logic 23 (1).
    A question dating to Mardešić and Prasolov’s 1988 work [S. Mardešić and A. V. Prasolov, Strong homology is not additive, Trans. Amer. Math. Soc. 307(2) (1988) 725–744], and motivating a considerable amount of set theoretic work in the years since, is that of whether it is consistent with the ZFC axioms for the higher derived limits [Formula: see text] [Formula: see text] of a certain inverse system [Formula: see text] indexed by [Formula: see text] to simultaneously vanish. An equivalent formulation (...)
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  10.  13
    The Hanf number for amalgamation of coloring classes.Alexei Kolesnikov & Chris Lambie-Hanson - 2016 - Journal of Symbolic Logic 81 (2):570-583.
  11.  15
    Knaster and Friends III: Subadditive Colorings.Chris Lambie-Hanson & Assaf Rinot - 2023 - Journal of Symbolic Logic 88 (3):1230-1280.
    We continue our study of strongly unbounded colorings, this time focusing on subadditive maps. In Part I of this series, we showed that, for many pairs of infinite cardinals $\theta < \kappa $, the existence of a strongly unbounded coloring $c:[\kappa ]^2 \rightarrow \theta $ is a theorem of $\textsf{ZFC}$. Adding the requirement of subadditivity to a strongly unbounded coloring is a significant strengthening, though, and here we see that in many cases the existence of a subadditive strongly unbounded coloring (...)
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  12.  20
    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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  13.  20
    Good and bad points in scales.Chris Lambie-Hanson - 2014 - Archive for Mathematical Logic 53 (7):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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  14.  28
    Bounded stationary reflection II.Chris Lambie-Hanson - 2017 - Annals of Pure and Applied Logic 168 (1):50-71.
  15.  14
    Indestructibility of some compactness principles over models of PFA.Radek Honzik, Chris Lambie-Hanson & Šárka Stejskalová - 2024 - Annals of Pure and Applied Logic 175 (1):103359.
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  16.  6
    Polish Space Partition Principles and the Halpern–Läuchli Theorem.Chris Lambie-Hanson & Andy Zucker - forthcoming - Journal of Symbolic Logic:1-19.
    The Halpern–Läuchli theorem, a combinatorial result about trees, admits an elegant proof due to Harrington using ideas from forcing. In an attempt to distill the combinatorial essence of this proof, we isolate various partition principles about products of perfect Polish spaces. These principles yield straightforward proofs of the Halpern–Läuchli theorem, and the same forcing from Harrington’s proof can force their consistency. We also show that these principles are not ZFC theorems by showing that they put lower bounds on the size (...)
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