Assaf Rinot
Rock / Metal / Logic

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

Tel Aviv, Israel

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   Contacting Assaf Rinot

   Teaching this year
        88-802: Walks on Ordinals

   General Info
I am a faculty member 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 set theoretic topology.
Status Married + 2
Trivia I was born on Paul Erdös' 65th birthday.
Erdös number 3
Co-authors Sakae Fuchino, Moti Gitik, Stevo Todorcevic.


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   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.
Chromatic number of graphs - large gaps, to appear in Combinatorica. DOI: 10.1007/s00493-014-3074-7.
Chain conditions of products, and weakly compact cardinals, Bull. Symbolic Logic, 20(3): 293-314, 2014.
Complicated colorings, Math. Res. Lett., 21(6), 1-22, 2014.

Hedetniemi's conjecture for uncountable graphs, to appear in J. Eur. Math. Soc.
Putting a diamond inside the square, to appear in Bull. Lond. Math. Soc.
Same Graph, Different Universe, submitted.

   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 Todorcevics CRM-Fields-PIMS Prize Lecture, Fields Notes, 13, Winter 2013.

Shelah's solution to Whitehead's problem (In hebrew).
Infinite combinatorial topology.
Covering properties: separating Menger from Hurewicz.
Surprisingly short.

   Contributed and Invited 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

   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