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Luzin set b-scale Distributive tree Large Cardinals square principles super-Souslin tree Axiom R Uniformization Chromatic number Kurepa Hypothesis Sierpinski's onto mapping principle Subadditive Ostaszewski square Almost-disjoint family Intersection model approachability ideal Parameterized proxy principle Hedetniemi's conjecture Cohen real sap nonmeager set Uniformly homogeneous Forcing weak Kurepa tree Souslin Tree Subtle cardinal Postprocessing function Absoluteness Countryman line SNR indecomposable filter Minimal Walks Vanishing levels Square-Brackets Partition Relations Generalized Clubs square Dowker space Knaster Forcing Axioms O-space PFA higher Baire space Poset Singular cofinality HOD Cardinal Invariants Analytic sets Singular Density transformations Partition Relations Cardinal function Amenable C-sequence Diamond-sharp Commutative projection system Erdos Cardinal Fast club Was Ulam right? Non-saturation Microscopic Approach Universal Sequences Subtle tree property Constructible Universe Martin's Axiom positive partition relation Fodor-type reflection Ascent Path Diamond AIM forcing Fat stationary set free Souslin tree specializable Souslin tree unbounded function Singular cardinals combinatorics Mandelbrot set GMA Shelah's Strong Hypothesis Aronszajn tree Whitehead Problem Ramsey theory over partitions Rado's conjecture Reflecting stationary set weak square L-space Strongly compact cardinal Rock n' Roll Iterated forcing P-Ideal Dichotomy Coherent tree Nonspecial tree Prikry-type forcing C-sequence Selective Ultrafilter Sigma-Prikry middle diamond Filter reflection diamond star Open Access Foundations Closed coloring coloring number Prevalent singular cardinals Chang's conjecture Strongly Luzin set Rainbow sets Diamond for trees Generalized descriptive set theory club_AD Weakly compact cardinal countably metacompact Lipschitz reduction Club Guessing strongly bounded groups xbox Sakurai's Bell inequality Almost Souslin reflection principles polarized partition relation Well-behaved magma Commutative cancellative semigroups Jonsson cardinal full tree Successor of Regular Cardinal Subnormal ideal Dushnik-Miller Erdos-Hajnal graphs Small forcing Ulam matrix OCA Hereditarily Lindelöf space stick projective Boolean algebra stationary reflection ZFC construction Respecting tree Almost countably chromatic tensor product graph Precaliber S-Space Knaster and friends free Boolean algebra stationary hitting weak diamond ccc Greatly Mahlo Successor of Singular Cardinal Uniformly coherent Slim tree Strong coloring very good scale Hindman's Theorem 54G20 Local Club Condensation. Reduced Power PFA(S)[S] incompactness Antichain regressive Souslin tree Ineffable cardinal
Author Archives: Assaf Rinot
Sums of triples in Abelian groups
Joint work with Ido Feldman. Abstract. Motivated by a problem in additive Ramsey theory, we extend Todorcevic’s partitions of three-dimensional combinatorial cubes to handle additional three-dimensional objects. As a corollary, we get that if the continuum hypothesis fails, then for … Continue reading
A club guessing toolbox I
Joint work with Tanmay Inamdar. Abstract. Club guessing principles were introduced by Shelah as a weakening of Jensen’s diamond. Most spectacularly, they were used to prove Shelah’s ZFC bound on the power of the first singular cardinal. These principles have … Continue reading
Ramsey theory over partitions II: Negative Ramsey relations and pump-up theorems
Joint work with Menachem Kojman and Juris Steprāns. Abstract. In this series of papers, we advance Ramsey theory of colorings over partitions. In this part, we concentrate on anti-Ramsey relations, or, as they are better known, strong colorings, and in … Continue reading
A new small Dowker space
Joint work with Roy Shalev and Stevo Todorcevic. Abstract. It is proved that if there exists a Luzin set, or if either the stick principle or
Was Ulam right? II: Small width and general ideals
Joint work with Tanmay Inamdar. Abstract. We continue our study of Sierpinski-type colourings. In contrast to the prequel paper, we focus here on colourings for ideals stratified by their completeness degree. In particular, improving upon Ulam’s theorem and its extension … Continue reading
Posted in Partition Relations, Publications
Tagged 03E02, 03E35, 03E55, C-sequence, Open Access, Subnormal ideal, Ulam matrix, Was Ulam right?
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MFO workshop in Set Theory, January 2022
I gave an invited talk at the Set Theory meeting in Obwerwolfach, January 2022. Talk Title: A dual of Juhasz’ question Abstract: Juhasz asked whether
Posted in Invited Talks
Tagged club_AD, Dowker space
Comments Off on MFO workshop in Set Theory, January 2022
Complicated colorings, revisited
Joint work with Jing Zhang. Abstract. In a paper from 1997, Shelah asked whether
Sigma-Prikry forcing III: Down to Aleph_omega
Joint work with Alejandro Poveda and Dima Sinapova. Abstract. We prove the consistency of the failure of the singular cardinals hypothesis at
Was Ulam right? I: Basic theory and subnormal ideals
Joint work with Tanmay Inamdar. Abstract. We introduce various coloring principles which generalize the so-called onto mapping principle of Sierpinski to larger cardinals and general ideals. We prove that these principles capture the notion of an Ulam matrix and allow … Continue reading
Knaster and friends III: Subadditive colorings
Joint work with Chris Lambie-Hanson. Abstract. We continue our study of strongly unbounded colorings, this time focusing on subadditive maps. In Part I of this series, we showed that, for many pairs of infinite cardinals
