#### Assaf Rinot - אסף רינות

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#### Web Name: Assaf Rinot - אסף רינות

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Assaf Rinot

**Rock / Metal / Logic**

**"The thought contains the possibility of the state of affairs which it thinks.**

What is thinkable is also possible."

What is thinkable is also possible."

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Contacting Assaf Rinot

Teaching this year 88-195: Discrete Mathematics88-202: Set Theory888212: An Introduction to Independence Proofs88-889: Set Theory Colloquium

General Info About

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.

Contact

Department of Mathematics

Bar-Ilan University

Ramat-Gan 5290002

Israel

(information for visitors) Status Married + 2

Trivia I was born on Paul Erdös' 65th birthday. Erdős number Co-authors Ari Meir Brodsky,James Cummings,Gabriel Fernandes,David J. Fernandez-Breton,Sakae Fuchino,Gunter Fuchs,Sy-David Friedman, Moti Gitik, Tanmay Inamdar,Menachem Kojman,Chris Lambie-Hanson,Maxwell Levine,Menachem Magidor,Miguel Moreno,Alejandro Poveda, Ralf Schindler, Roy Shalev,Dima Sinapova,Juris Steprāns, Stevo Todorcevic,Jing Zhang.

Blurb

Research papers ▷ On the consistency strength of the Milner-Sauer conjecture, Ann. PureAppl. Logic, 140(1-3): 110-119, 2006. ▷ Aspects of singular cofinality, Contrib. Discrete Math.,2(2): 185-204, 2007.

▷ 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. PureAppl. 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.

To appear ▷ A guessing principle from a Souslin tree, with applications to topology (with R. Shalev), Topology Appl., accepted September 2021. ▷ Sigma-Prikry forcing II: Iteration scheme (with A. Poveda and D. Sinapova), J. Math. Logic, accepted December 2021. ▷ Was Ulam right? I: Basic theory and subnormal ideals (with T. Inamdar), Topology Appl., accepted December 2021. ▷ Ramsey theory over partitions III: Strongly Luzin sets and partition relations (with M. Kojman and J. Steprans), Proc. Amer. Math. Soc., accepted April 2022. ▷ Ramsey theory over partitions II: Negative Ramsey relations and pump-up theorems (with M. Kojman and J. Steprans), Israel J. Math., accepted May 2022. ▷ Ramsey theory over partitions I: Positive Ramsey relations from forcing axioms (with M. Kojman and J. Steprans), Israel J. Math., accepted May 2022. ▷ Stongest transformations (with J. Zhang), Combinatorica, accepted May 2022. ▷ Knaster and friends III: Subadditive colorings (with C. Lambie-Hanson), J. Symbolic Logic, accepted June 2022.

Preprints ▷ Sigma-Prikry forcing III: Down to Aleph_omega (with A. Poveda and D. Sinapova), submitted October 2021. ▷ Complicated colorings, revisited (with J. Zhang), submitted February 2022. ▷ Was Ulam right? II: Small width and general ideals (with T. Inamdar), submitted March 2022. ▷ A new small Dowker space (with R. Shalev and S. Todorcevic), submitted April 2022. ▷ A club guessing toolbox I (with T. Inamdar), submitted July 2022.

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.

Notes ▷ A note on the ideal I[S;λ]. ▷ How to construct a Souslin tree the right way. ▷ Shelah's solution to Whitehead's problem (In hebrew). ▷ Infinite combinatorial topology.

▷ Covering properties: separating Menger from Hurewicz. ▷ Surprisingly short.

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Selected Talks Aug 8 2005 Logic in Hungary 2005 Budapest May 5 2006 2006 Annual conference of the IMU Neve Ilan Feb 19 2007 Workshop on Set Theory and its Applications Rehovot Mar 5 2007 Singular Cardinal Combinatorics and Inner Model Theory Gainesville, Florida Jan 25 2008 Young Researchers in Set Theory workshop Bonn Mar 27 2009 Boise Extravaganza in Set Theory 18 Boise, Idaho Jun 18 2009 ESI Workshop on Large Cardinals and Descriptive Set Theory Vienna Aug 02 2009 Logic Colloquium 2009 Sofia Jul 28 2010 Logic Colloquium 2010 Paris Oct 07 2010 The 11th International Workshop on Set Theory in Luminy Marseille Mar 22 2011 Young Researchers in Set Theory 2011 Königswinter Dec 11 2011 2011 CMS Winter Meeting Toronto Mar 31 2012 2012 ASL North American Annual Meeting Madison, Wisconsin Sep 26 2013 ESI Workshop on Large Cardinals and Forcing Vienna Jan 14 2014 Set Theory Oberwolfach Mar 4 2014 INFTY Final Conference Bonn April 1 2015 Forcing and its Applications - Retrospective Workshop Toronto May 31 2015 A conference in honour of Arthur Apter and Moti Gitik Pittsburgh Sep 26 2015 P.O.I Workshop in pure and descriptive set theory Torino July 20 2016 7th European Congress of Mathematics Berlin Sep 12 2016 Set Theory and its Applications in Topology Oaxaca Feb 13 2017 Set Theory Oberwolfach Mar 21 2017 2017 ASL North American Meeting Boise, Idaho July 4--6 2017 6th European Set Theory Conference Budapest Oct 10 2017 The 14th International Workshop on Set Theory in Luminy Marseille June 25--26 2018 Young Researchers in Set Theory 2018 Lausanne January 22 2019 Arctic Set Theory Workshop 4 Kilpisjarvi May 13 2019 50 Years of Set Theory in Toronto Toronto September 23 2019 The 15th International Workshop on Set Theory in Luminy Marseille April 2020 Set Theory Oberwolfach January 10 2022 Set Theory Oberwolfach January 28 2023 Winter School in Abstract Analysis 2023 Hejnice

Attended Meetings March 2004 Cardinal Arithmetic at Work Jerusalem May 2006 Workshop on the Urysohn space Beer Sheva March 2007 The 2007 Annual Meeting of the ASL Gainesville, Florida April 2009 Young Researchers in Set Theory 2009 Bellaterra May 2009 The 2009 Annual meeting of the IMU Rehovot February 2010 Young Researchers in Set Theory 2010 Raach am Hochgebirge October 2011 Proper forcing remastered Chicago July-December 2012 Thematic Program on Forcing and its Applications Toronto May 2013 2013 ASL North American Annual Meeting Waterloo May 2013 AIM SQuaRE: Singular Cardinals Combinatorics Palo Alto October 2014 AIM SQuaRE: Singular Cardinals Combinatorics 2 Palo Alto October 2015 Compactness, Incompactness and Canonical Structures Jerusalem January 2016 AIM SQuaRE: Singular Cardinals Combinatorics 3 San Jose February 2016 Menachem Magidor 70th Birthday Conference Jerusalem April 2018 Set Theory, Model Theory and Applications Eilat July 2022 Avances in Set Theory 2022 Jerusalem

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