Prof. Assaf Rinot

Prof. Assaf Rinot


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, Arch. Math. Logic, 56(7-8): 783-796, 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), to appear in Trans. Amer. Math. Soc..
Ordinal definable subsets of singular cardinals (with J. Cummings, S. D. Friedman, M. Magidor, and D. Sinapova), to appear in Isr. J. Math.
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), 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), submitted December 2016.
Distributive Aronszajn trees (with A. M. Brodsky), submitted April 2017.
A forcing axiom deciding the generalized Souslin Hypothesis (with C. Lambie-Hanson), submitted July 2017.


combinatorial set theory, especially around the combinatorics of singular cardinals