Assaf Rinot
Rock / Metal / Logic

"The thought contains the possibility of the state of affairs which it thinks.
What is thinkable is also possible."

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   Contacting Assaf Rinot

   Teaching this year
        88-303: Mathematical Logic
        88-202: Set Theory

   General Info
I am an Associate 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.
Department of Mathematics
Bar-Ilan University
Ramat-Gan 5290002
Status Married + 2
Trivia I was born on Paul Erdös' 65th birthday.
Erdös number 2
Co-authors Ari Meir Brodsky, James Cummings, David J. Fernandez Breton, Sakae Fuchino, Gunter Fuchs, Sy-David Friedman, Moti Gitik, Chris Lambie-Hanson, Menachem Magidor, Ralf Schindler, Dima Sinapova, Stevo Todorcevic.

Menacham Magidor Bitrthday Conference

Young Set Theory in Jerusalem


.מתמטיקה עושים ביסודיות, או לא עושים בכלל

   Research papers
On the consistency strength of the Milner-Sauer conjecture, Ann. Pure Appl. 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 HypothesisProc. 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): 1-82, 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.

   To appear
Ordinal definable subsets of singular cardinals (with J. Cummings, S.-D. Friedman, M. Magidor, and D. Sinapova), to appear in Isr. J. Math.
More notions of forcing add a Souslin tree (with A. M. Brodsky), to appear in Notre Dame J. Form. Log.
Reflection on the coloring and chromatic numbers (with C. Lambie-Hanson), to appear in Combinatorica.
The eightfold way (with J. Cummings, S.-D. Friedman, M. Magidor, and D. Sinapova), to appear in J. Symbolic Logic.
Weak square and stationary reflection (with G. Fuchs), to appear in Acta. Math. Hungar.
A forcing axiom deciding the generalized Souslin Hypothesis (with C. Lambie-Hanson), to appear in Canad. J. Math.

Distributive Aronszajn trees (with A. M. Brodsky), submitted April 2017.
A remark on Schimmerling's question (with A. M. Brodsky), submitted November 2017.

   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.

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.

   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
upcoming Young Researchers in Set Theory 2018 Lausanne

   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
upcoming Set Theory, Model Theory and Applications Eilat