ד"ר אסף רינות

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ד"ר אסף רינות
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פירסומים

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.
Hedetniemi's conjecture for uncountable graphs, J. Eur. Math. Soc., 19(1): 289-298, 2017.
Same Graph, Different Universe, to appear in Arch. Math. Logic.
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), to appear in J. Symbolic Logic.
A Microscopic approach to Souslin-tree constructions. Part I (with A. M. Brodsky), to appear in Ann. Pure Appl. Logic.
Strong failures of higher analogs of Hindman's Theorem (with D. J. Fernandez Breton), to appear in Trans. Amer. Math. Soc..
Ordinal definable subsets of singular cardinals (with J. Cummings, S. D. Friedman, M. Magidor, and D. Sinapova), submitted April 2016.
Higher Souslin trees and the GCH, revisited, Adv. Math., 311(c): 510-531, 2017.
More notions of forcing add a Souslin tree (with A. M. Brodsky), submitted July 2016.
Reflection on the coloring and chromatic numbers (with C. Lambie-Hanson), submitted December 2016.
The eightfold way (with J. Cummings, S.-D. Friedman, M. Magidor, and D. Sinapova), submitted December 2016.
Distributive Aronszajn trees (with A. M. Brodsky), submitted April 2017.

תחומי מחקר

תורת הקבוצות עם דגש על קומבינטוריקה אינסופית. סדרים חלקיים, תורת אנטי-רמזי למונים לא בני-מניה, ויישומים של תורת מבנה עדין לפתרון בעיות בטופולוגיה, תורת הגרפים האינסופיים, ותחומים נוספים.