Assaf Rinot
Rock / Metal / Logic |
 |
 |
"The thought contains the possibility of the state of affairs which it thinks.
What is thinkable is also possible."
|
| Visit my Blog
|
|
 |
|
|
|
| General Info |
About
|
I am a Professor 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 infinite graph theory.
|
Contact
|
Department of Mathematics
Bar-Ilan University
Ramat-Gan 5290002
Israel
(information for visitors) |
| Status |
Married + 2
|
| Trivia |
I was born on Paul Erdös' 65th birthday. |
| Erdős number |
|
| Co-authors |
Ari Meir Brodsky,
Rodrigo Carvalho,
James Cummings,
Ido Feldman,
Gabriel Fernandes,
David Fernandez-Breton,
Sakae Fuchino,
Gunter Fuchs,
Sy-David Friedman,
Moti Gitik,
Tanmay Inamdar,
Sittinon Jirattikansakul,
Menachem Kojman,
Ziemek Kostana,
Chris Lambie-Hanson,
Maxwell Levine,
Menachem Magidor,
Miguel Moreno,
Inbar Oren,
Márk Poór,
Alejandro Poveda,
Ralf Schindler,
Roy Shalev,
Saharon Shelah,
Dima Sinapova,
Juris Steprāns,
Stevo Todorcevic,
Shira Yadai,
Zhixing You,
Jiachen Yuan,
Jing Zhang.
|
|
|
![]() |
| Blurb |
|
.מתמטיקה עושים ביסודיות, או לא עושים בכלל
|
|
| 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 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. |
| ▷ Same Graph, Different Universe, Arch. Math. Logic, 56(7-8): 783-796, 2017. |
| ▷ Hedetniemi's conjecture for uncountable graphs, J. Eur. Math. Soc, 19(1): 285-298, 2017. |
| ▷ Reduced powers of Souslin trees (with A. M. Brodsky), Forum Math. Sigma, 5(e2): 82pp, 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), Trans. Amer. Math. Soc., 369(12): 8939-8966, 2017. |
| ▷ Higher Souslin trees and the GCH, revisited, Adv. Math., 311(c): 510-531, 2017. |
| ▷ Ordinal definable subsets of singular cardinals (with J. Cummings, S.-D. Friedman, M. Magidor, and D. Sinapova), Isr. J. Math., 226(2), 781-804, 2018. |
| ▷ The eightfold way (with J. Cummings, S.-D. Friedman, M. Magidor, and D. Sinapova), J. Symbolic Logic, 83(1): 349-371, 2018. |
| ▷ Weak square and stationary reflection (with G. Fuchs), Acta. Math. Hungar., 155(2), 393-405, 2018. |
| ▷ Knaster and friends I: Closed colorings and precalibers (with C. Lambie-Hanson), Algebra Universalis, 79(4), Art. 90, 39 pp., 2018. |
| ▷ Distributive Aronszajn trees (with A. M. Brodsky), Fund. Math., 245(3): 217-291, 2019. |
| ▷ A forcing axiom deciding the generalized Souslin Hypothesis (with C. Lambie-Hanson), Canad. J. Math., 71(2): 437-470, 2019. |
| ▷ Reflection on the coloring and chromatic numbers (with C. Lambie-Hanson), Combinatorica, 39(1): 165-214, 2019. |
| ▷ Souslin trees at successors of regular cardinals, Math. Log. Q., 65(2): 200-204, 2019. |
| ▷ More notions of forcing add a Souslin tree (with A. M. Brodsky), Notre Dame J. Form. Log., 60(3): 437-455, 2019. |
| ▷ A remark on Schimmerling's question (with A. M. Brodsky), Order, 36(3): 525-561, 2019. |
| ▷ Partitioning a reflecting stationary set (with M. Levine), Proc. Amer. Math. Soc., 148(8):3551-3565, 2020. |
| ▷ Inclusion modulo nonstationary (with G. Fernandes and M. Moreno), Monatsh. Math., 192(4): 827-851, 2020. |
| ▷ A Microscopic approach to Souslin-tree constructions. Part II (with A. M. Brodsky), Ann. Pure Appl. Logic, 172(5): 102904, 65pp, 2021. |
| ▷ Knaster and friends II: The C-sequence number (with C. Lambie-Hanson), J. Math. Logic, 21(1): 2150002, 54pp, 2021. |
| ▷ Transformations of the transfinite plane (with J. Zhang), Forum Math. Sigma, 9(e16), 25pp, 2021. |
| ▷ Sigma-Prikry forcing I: The axioms (with A. Poveda and D. Sinapova), Canad. J. Math., 73(5): 1205-1238, 2021. |
| ▷ Fake reflection (with G. Fernandes and M. Moreno), Isr. J. Math., 245(1): 295-345, 2021. |
| ▷ On the ideal J[kappa], Ann. Pure Appl. Logic, 173(2): 103055, 13pp, 2022. |
| ▷ Sigma-Prikry forcing II: Iteration scheme (with A. Poveda and D. Sinapova), J. Math. Logic, 22(3): 2150019, 59pp, 2022. |
| ▷ Was Ulam right? I: Basic theory and subnormal ideals (with T. Inamdar), Topology Appl., 323(C): 108287, 53pp, 2023. |
| ▷ A guessing principle from a Souslin tree, with applications to topology (with R. Shalev), Topology Appl., 323(C): 108296, 29pp, 2023. |
| ▷ Complicated colorings, revisited (with J. Zhang), Ann. Pure Appl. Logic, 174(4): 103243, 11pp, 2023. |
| ▷ Sums of triples in Abelian groups (with I. Feldman), Mathematika, 69(3): 622-664, 2023. |
| ▷ Strongest transformations (with J. Zhang), Combinatorica, 43(1): 149-185, 2023. |
| ▷ Knaster and friends III: Subadditive colorings (with C. Lambie-Hanson), J. Symbolic Logic, 88(3): 1230-1280, 2023. |
| ▷ Ramsey theory over partitions III: Strongly Luzin sets and partition relations (with M. Kojman and J. Steprans), Proc. Amer. Math. Soc., 151(1): 369-384, 2023. |
| ▷ Sigma-Prikry forcing III: Down to Aleph_omega (with A. Poveda and D. Sinapova), Adv. Math., 435: 109377, 84pp, 2023. |
| ▷ A new small Dowker space (with R. Shalev and S. Todorcevic), Period. Math. Hung., 88(1): 102-117, 2024. |
| ▷ Was Ulam right? II: Small width and general ideals (with T. Inamdar), Algebra Universalis, 85(2): 14, 47pp, 2024. |
| ▷ Ramsey theory over partitions I: Positive Ramsey relations from forcing axioms (with M. Kojman and J. Steprans), Israel J. Math., 261(1): 205-222, 2024 |
| ▷ Ramsey theory over partitions II: Negative Ramsey relations and pump-up theorems (with M. Kojman and J. Steprans), Israel J. Math., 261(1): 223-247, 2024. |
| ▷ Full Souslin trees at small cardinals (with S. Yadai and Z. You), J. Lond. Math. Soc., 110(1): e12957, 26pp, 2024. |
|
| 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 Todorcevic’s CRM-Fields-PIMS Prize Lecture, Fields Notes, 13, Winter 2013. |
| ▷ Review on Eisworth's handbook chapter, AMS Math. Reviews, 2016. |
| ▷ May the successor of a singular cardinal be Jonsson?, preprint November 2023. |
|
| Find paper by serial number |
|
