Assaf Rinot
Rock / Metal / Logic |
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"The thought contains the possibility of the state of affairs which it thinks. What is thinkable is also possible."
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General Info |
About
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I am a Professor in the Department of Mathematics, Bar-Ilan University. |
Research interests |
My principal fields of research are Mathematical Logic and Set Theory.
I am mostly interested in infinitary combinatorics: partition relations, singular cardinals combinatorics, and infinite graph theory.
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Contact
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Department of Mathematics Bar-Ilan University Ramat-Gan 5290002 Israel (information for visitors) |
Status |
Married + 2
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Trivia |
I was born on Paul Erdös' 65th birthday. |
Erdős number |
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Co-authors |
Ari Meir Brodsky,
Rodrigo Carvalho,
James Cummings,
Ido Feldman,
Gabriel Fernandes,
David Fernandez-Breton,
Sakae Fuchino,
Gunter Fuchs,
Sy-David Friedman,
Moti Gitik,
Tanmay Inamdar,
Menachem Kojman,
Ziemek Kostana,
Chris Lambie-Hanson,
Maxwell Levine,
Menachem Magidor,
Miguel Moreno,
Márk Poór,
Alejandro Poveda,
Ralf Schindler,
Roy Shalev,
Saharon Shelah,
Dima Sinapova,
Juris Steprāns,
Stevo Todorcevic,
Shira Yadai,
Zhixing You,
Jing Zhang.
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Blurb |
.מתמטיקה עושים ביסודיות, או לא עושים בכלל
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Research papers |
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▷ On the consistency strength of the Milner-Sauer conjecture, Ann. Pure Appl. Logic, 140(1-3): 110-119, 2006.
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▷ Aspects of singular cofinality, Contrib. Discrete Math., 2(2): 185-204, 2007.
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▷ Antichains in partially ordered sets of singular cofinality, Arch. Math. Logic, 46(5-6): 457-464, 2007. |
▷ On topological spaces of singular density and minimal weight, Topology Appl., 155(3): 135-140, 2007. |
▷ A topological reflection principle equivalent to Shelah's Strong Hypothesis, Proc. Amer. Math. Soc., 136(12): 4413-4416, 2008. |
▷ A cofinality-preserving small forcing may introduce a special Aronszajn tree, Arch. Math. Logic, 48(8): 817-823, 2009. |
▷ A relative of the approachability ideal, diamond and non-saturation, J. Symbolic Logic, 75(3): 1035-1065, 2010. |
▷ On guessing generalized clubs at the successors of regulars, Ann. Pure Appl. Logic, 162(7): 566-577, 2011. |
▷ Openly generated Boolean algebras and the Fodor-type Reflection Principle (with S. Fuchino), Fund. Math., 212(3): 261-283, 2011. |
▷ The failure of diamond on a reflecting stationary set (with M. Gitik), Trans. Amer. Math. Soc., 364(4): 1771-1795, 2012. |
▷ Transforming rectangles into squares, with applications to strong colorings, Adv. Math., 231(2): 1085-1099, 2012. |
▷ Rectangular square-bracket operation for successor of regular cardinals (with S. Todorcevic), Fund. Math., 220(2): 119-128, 2013. |
▷ The Ostaszewski square, and homogeneous Souslin trees, Isr. J. Math, 199(2): 975-1012, 2014. |
▷ Chain conditions of products, and weakly compact cardinals, Bull. Symbolic Logic, 20(3): 293-314, 2014. |
▷ Complicated colorings, Math. Res. Lett., 21(6): 1367–1388, 2014. |
▷ Chromatic number of graphs - large gaps, Combinatorica, 35(2): 215-233, 2015. |
▷ Putting a diamond inside the square, Bull. Lond. Math. Soc., 47(3): 436-442, 2015. |
▷ Same Graph, Different Universe, Arch. Math. Logic, 56(7-8): 783-796, 2017. |
▷ Hedetniemi's conjecture for uncountable graphs, J. Eur. Math. Soc, 19(1): 285-298, 2017. |
▷ Reduced powers of Souslin trees (with A. M. Brodsky), Forum Math. Sigma, 5(e2): 82pp, 2017. |
▷ Square with built-in diamond-plus (with R. D. Schindler), J. Symbolic Logic, 82(3): 809-833, 2017. |
▷ A Microscopic approach to Souslin-tree constructions. Part I (with A. M. Brodsky), Ann. Pure Appl. Logic, 168(11): 1949-2007, 2017. |
▷ Strong failures of higher analogs of Hindman's Theorem (with D. J. Fernandez Breton), Trans. Amer. Math. Soc., 369(12): 8939-8966, 2017. |
▷ Higher Souslin trees and the GCH, revisited, Adv. Math., 311(c): 510-531, 2017. |
▷ Ordinal definable subsets of singular cardinals (with J. Cummings, S.-D. Friedman, M. Magidor, and D. Sinapova), Isr. J. Math., 226(2), 781-804, 2018. |
▷ The eightfold way (with J. Cummings, S.-D. Friedman, M. Magidor, and D. Sinapova), J. Symbolic Logic, 83(1): 349-371, 2018. |
▷ Weak square and stationary reflection (with G. Fuchs), Acta. Math. Hungar., 155(2), 393-405, 2018. |
▷ Knaster and friends I: Closed colorings and precalibers (with C. Lambie-Hanson), Algebra Universalis, 79(4), Art. 90, 39 pp., 2018. |
▷ Distributive Aronszajn trees (with A. M. Brodsky), Fund. Math., 245(3): 217-291, 2019. |
▷ A forcing axiom deciding the generalized Souslin Hypothesis (with C. Lambie-Hanson), Canad. J. Math., 71(2): 437-470, 2019. |
▷ Reflection on the coloring and chromatic numbers (with C. Lambie-Hanson), Combinatorica, 39(1): 165-214, 2019. |
▷ Souslin trees at successors of regular cardinals, Math. Log. Q., 65(2): 200-204, 2019. |
▷ More notions of forcing add a Souslin tree (with A. M. Brodsky), Notre Dame J. Form. Log., 60(3): 437-455, 2019. |
▷ A remark on Schimmerling's question (with A. M. Brodsky), Order, 36(3): 525-561, 2019. |
▷ Partitioning a reflecting stationary set (with M. Levine), Proc. Amer. Math. Soc., 148(8):3551-3565, 2020. |
▷ Inclusion modulo nonstationary (with G. Fernandes and M. Moreno), Monatsh. Math., 192(4): 827-851, 2020. |
▷ A Microscopic approach to Souslin-tree constructions. Part II (with A. M. Brodsky), Ann. Pure Appl. Logic, 172(5): 102904, 65pp, 2021. |
▷ Knaster and friends II: The C-sequence number (with C. Lambie-Hanson), J. Math. Logic, 21(1): 2150002, 54pp, 2021. |
▷ Transformations of the transfinite plane (with J. Zhang), Forum Math. Sigma, 9(e16), 25pp, 2021. |
▷ Sigma-Prikry forcing I: The axioms (with A. Poveda and D. Sinapova), Canad. J. Math., 73(5): 1205-1238, 2021. |
▷ Fake reflection (with G. Fernandes and M. Moreno), Isr. J. Math., 245(1): 295-345, 2021. |
▷ On the ideal J[kappa], Ann. Pure Appl. Logic, 173(2): 103055, 13pp, 2022. |
▷ Sigma-Prikry forcing II: Iteration scheme (with A. Poveda and D. Sinapova), J. Math. Logic, 22(3): 2150019, 59pp, 2022. |
▷ Was Ulam right? I: Basic theory and subnormal ideals (with T. Inamdar), Topology Appl., 323(C): 108287, 53pp, 2023. |
▷ A guessing principle from a Souslin tree, with applications to topology (with R. Shalev), Topology Appl., 323(C): 108296, 29pp, 2023. |
▷ Complicated colorings, revisited (with J. Zhang), Ann. Pure Appl. Logic, 174(4): 103243, 11pp, 2023. |
▷ Sums of triples in Abelian groups (with I. Feldman), Mathematika, 69(3): 622-664, 2023. |
▷ Strongest transformations (with J. Zhang), Combinatorica, 43(1): 149-185, 2023. |
▷ Knaster and friends III: Subadditive colorings (with C. Lambie-Hanson), J. Symbolic Logic, 88(3): 1230-1280, 2023. |
▷ Ramsey theory over partitions III: Strongly Luzin sets and partition relations (with M. Kojman and J. Steprans), Proc. Amer. Math. Soc., 151(1): 369-384, 2023. |
▷ Sigma-Prikry forcing III: Down to Aleph_omega (with A. Poveda and D. Sinapova), Adv. Math., 435: 109377, 84pp, 2023. |
▷ Was Ulam right? II: Small width and general ideals (with T. Inamdar), Algebra Universalis, 85(2): 14, 47pp, 2024. |
▷ A new small Dowker space (with R. Shalev and S. Todorcevic), Period. Math. Hung., 88(1): 102-117, 2024. |
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Preprints |
▷ A club guessing toolbox I (with T. Inamdar), submitted July 2022. |
▷ A counterexample related to a theorem of Komjath and Weiss (with R. Carvalho), submitted June 2023. |
▷ A Shelah group in ZFC (with M. Poór), submitted July 2023. |
▷ Full Souslin trees at small cardinals (with S. Yadai and Z. You), submitted July 2023. |
▷ The vanishing levels of a tree (with S. Yadai and Z. You), submitted September 2023. |
▷ Diamond on ladder systems and countably metacompact topological spaces (with R. Carvalho and T. Inamdar), submitted December 2023. |
▷ Squares, ultrafilters and forcing axioms (with C. Lambie-Hanson and J. Zhang), submitted January 2024. |
▷ Proxy principles in combinatorial set theory (with A. Brodsky and S. Yadai), submitted February 2024. |
▷ Diamond on Kurepa trees (with Z. Kostana and S. Shelah), submitted April 2024. |
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Surveys and Reviews |
▷ Jensen's diamond principle and its relatives, Set Theory and Its Applications, Contemp. Math., 533: 125-156, Amer. Math. Soc., Providence, RI, 2011. |
▷ The search for diamonds, Bull. Symbolic Logic, 16(3): 420-423, 2010. |
▷ Stevo Todorcevic’s CRM-Fields-PIMS Prize Lecture, Fields Notes, 13, Winter 2013. |
▷ Review on Eisworth's handbook chapter, AMS Math. Reviews, 2016. |
▷ May the successor of a singular cardinal be Jonsson?, preprint November 2023. |
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