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  1. New combinatorial principle on singular cardinals and normal ideals.Toshimichi Usuba - 2018 - Mathematical Logic Quarterly 64 (4-5):395-408.
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  • Square with built-in diamond-plus.Assaf Rinot & Ralf Schindler - 2017 - Journal of Symbolic Logic 82 (3):809-833.
    We formulate combinatorial principles that combine the square principle with various strong forms of the diamond principle, and prove that the strongest amongst them holds inLfor every infinite cardinal.As an application, we prove that the following two hold inL:1.For every infinite regular cardinalλ, there exists a special λ+-Aronszajn tree whose projection is almost Souslin;2.For every infinite cardinalλ, there exists arespectingλ+-Kurepa tree; Roughly speaking, this means that this λ+-Kurepa tree looks very much like the λ+-Souslin trees that Jensen constructed inL.
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  • Magidor–Malitz reflection.Yair Hayut - 2017 - Archive for Mathematical Logic 56 (3-4):253-272.
    In this paper we investigate the consistency and consequences of the downward Löwenheim–Skolem–Tarski theorem for extension of the first order logic by the Magidor–Malitz quantifier. We derive some combinatorial results and improve the known upper bound for the consistency of Chang’s conjecture at successor of singular cardinals.
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  • 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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  • A microscopic approach to Souslin-tree constructions, Part I.Ari Meir Brodsky & Assaf Rinot - 2017 - Annals of Pure and Applied Logic 168 (11):1949-2007.
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  • In memoriam: James Earl Baumgartner (1943–2011).J. A. Larson - 2017 - Archive for Mathematical Logic 56 (7):877-909.
    James Earl Baumgartner (March 23, 1943–December 28, 2011) came of age mathematically during the emergence of forcing as a fundamental technique of set theory, and his seminal research changed the way set theory is done. He made fundamental contributions to the development of forcing, to our understanding of uncountable orders, to the partition calculus, and to large cardinals and their ideals. He promulgated the use of logic such as absoluteness and elementary submodels to solve problems in set theory, he applied (...)
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  • Characterizing large cardinals in terms of layered posets.Sean Cox & Philipp Lücke - 2017 - Annals of Pure and Applied Logic 168 (5):1112-1131.
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  • Square and Delta reflection.Laura Fontanella & Yair Hayut - 2016 - Annals of Pure and Applied Logic 167 (8):663-683.
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  • Restrictions on forcings that change cofinalities.Yair Hayut & Asaf Karagila - 2016 - Archive for Mathematical Logic 55 (3-4):373-384.
    In this paper we investigate some properties of forcing which can be considered “nice” in the context of singularizing regular cardinals to have an uncountable cofinality. We show that such forcing which changes cofinality of a regular cardinal, cannot be too nice and must cause some “damage” to the structure of cardinals and stationary sets. As a consequence there is no analogue to the Prikry forcing, in terms of “nice” properties, when changing cofinalities to be uncountable.
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  • Complicated colorings, revisited.Assaf Rinot & Jing Zhang - 2023 - Annals of Pure and Applied Logic 174 (4):103243.
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  • Squares, ascent paths, and chain conditions.Chris Lambie-Hanson & Philipp Lücke - 2018 - Journal of Symbolic Logic 83 (4):1512-1538.
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  • 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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  • 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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  • A note on edge colorings and trees.Adi Jarden & Ziv Shami - 2022 - Mathematical Logic Quarterly 68 (4):447-457.
    We point out some connections between existence of homogenous sets for certain edge colorings and existence of branches in certain trees. As a consequence, we get that any locally additive coloring (a notion introduced in the paper) of a cardinal κ has a homogeneous set of size κ provided that the number of colors μ satisfies. Another result is that an uncountable cardinal κ is weakly compact if and only if κ is regular, has the tree property, and for each (...)
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