# Prof. Assaf Rinot

Prof.

Telephone:

03-5318272

Fax:

03-7384057

Email:

rinotas

Office:

Building 216, Room 109

Website/s:

## Publications

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 Hypothesis, Proc. 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. |

## Research

combinatorial set theory, especially around the combinatorics of singular cardinals

- Last modified: 11/09/2017