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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General Info 
About

I am a faculty member in the Department of Mathematics, BarIlan 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.

Contact

Department of Mathematics BarIlan University RamatGan 52900 Israel 
Status 
Married + 2

Trivia 
I was born on Paul Erdös' 65th birthday. 
Erdös number 

Coauthors 
Ari Meir Brodsky,
James Cummings,
David J. Fernandez Breton,
Sakae Fuchino,
SyDavid Friedman,
Moti Gitik,
Chris LambieHanson,
Menachem Magidor,
Ralf Schindler,
Dima Sinapova,
Stevo Todorcevic. 



Blurb 
.מתמטיקה עושים ביסודיות, או לא עושים בכלל


Research papers 


▷ On the consistency strength of the MilnerSauer conjecture, Ann. Pure Appl. Logic, 140(13): 110119, 2006.

▷ Aspects of singular cofinality, Contrib. Discrete Math., 2(2): 185204, 2007.

▷ Antichains in partially ordered sets of singular cofinality, Arch. Math. Logic, 46(56): 457464, 2007. 
▷ On topological spaces of singular density and minimal weight, Topology Appl., 155(3): 135140, 2007. 
▷ A topological reflection principle equivalent to Shelah's Strong Hypothesis, Proc. Amer. Math. Soc., 136(12): 44134416, 2008. 
▷ A cofinalitypreserving small forcing may introduce a special Aronszajn tree, Arch. Math. Logic, 48(8): 817823, 2009. 
▷ A relative of the approachability ideal, diamond and nonsaturation, J. Symbolic Logic, 75(3): 10351065, 2010. 
▷ On guessing generalized clubs at the successors of regulars, Ann. Pure Appl. Logic, 162(7): 566577, 2011. 
▷ Openly generated Boolean algebras and the Fodortype Reflection Principle (with S. Fuchino), Fund. Math., 212(3): 261283, 2011. 
▷ The failure of diamond on a reflecting stationary set (with M. Gitik), Trans. Amer. Math. Soc., 364(4): 17711795, 2012. 
▷ Transforming rectangles into squares, with applications to strong colorings, Adv. Math., 231(2): 10851099, 2012. 
▷ Rectangular squarebracket operation for successor of regular cardinals (with S. Todorcevic), Fund. Math., 220(2): 119128, 2013. 
▷ The Ostaszewski square, and homogeneous Souslin trees, Isr. J. Math, 199(2): 9751012, 2014. 
▷ Chain conditions of products, and weakly compact cardinals, Bull. Symbolic Logic, 20(3): 293314, 2014. 
▷ Complicated colorings, Math. Res. Lett., 21(6): 1367–1388, 2014. 
▷ Chromatic number of graphs  large gaps, Combinatorica, 35(2): 215233, 2015. 
▷ Putting a diamond inside the square, Bull. Lond. Math. Soc., 47(3): 436442, 2015. 
▷ Hedetniemi's conjecture for uncountable graphs, J. Eur. Math. Soc, 19(1): 285298, 2017. 
▷ Reduced powers of Souslin trees (with A. M. Brodsky), Forum Math. Sigma, 5(e2): 182, 2017. 
▷ Higher Souslin trees and the GCH, revisited, Adv. Math., 311(c): 510531, 2017. 

Preprints 
▷ A Microscopic approach to Souslintree constructions. Part I (with A. M. Brodsky), submitted December 2015. 
▷ Ordinal definable subsets of singular cardinals (with J. Cummings, S.D. Friedman, M. Magidor, and D. Sinapova), submitted April 2016. 
▷ More notions of forcing add a Souslin tree (with A. M. Brodsky), submitted July 2016. 
▷ Reflection on the coloring and chromatic numbers (with C. LambieHanson), submitted December 2016. 
▷ The eightfold way (with J. Cummings, S.D. Friedman, M. Magidor, and D. Sinapova), submitted December 2016. 

Surveys and Reviews 
▷ Jensen's diamond principle and its relatives, Set Theory and Its Applications, Contemp. Math., 533: 125156, Amer. Math. Soc., Providence, RI, 2011. 
▷ The search for diamonds, Bull. Symbolic Logic, 16(3): 420423, 2010. 
▷ Stevo Todorcevic’s CRMFieldsPIMS Prize Lecture, Fields Notes, 13, Winter 2013. 
▷ Review on Eisworth's handbook chapter, AMS Math. Reviews, 2016. 

