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Keywords
Almost-disjoint family Distributive tree projective Boolean algebra indecomposable ultrafilter Non-saturation Rado's conjecture Sakurai's Bell inequality Reduced Power weak square Rainbow sets HOD Lipschitz reduction Vanishing levels Souslin Tree 54G20 Nonspecial tree Successor of Singular Cardinal full tree incompactness club_AD PFA Closed coloring ZFC construction C-sequence square principles xbox Martin's Axiom free Boolean algebra Was Ulam right? positive partition relation SNR Singular Density Countryman line Coherent tree nonmeager set Prikry-type forcing P-Ideal Dichotomy Greatly Mahlo super-Souslin tree Fat stationary set Poset Well-behaved magma higher Baire space transformations Ascent Path Amenable C-sequence Dowker space Knaster and friends Minimal Walks Generalized descriptive set theory Whitehead Problem Universal Sequences GMA Hereditarily Lindelöf space b-scale Chromatic number coloring number Precaliber stick Analytic sets Uniformization Weakly compact cardinal Erdos-Hajnal graphs Filter reflection Strongly Luzin set square regressive Souslin tree weak diamond Uniformly coherent Iterated forcing Luzin set Singular cofinality Ostaszewski square Diamond-sharp sap Selective Ultrafilter middle diamond Forcing Diamond for trees Slim tree Hindman's Theorem Fodor-type reflection Antichain unbounded function Intersection model Foundations Erdos Cardinal Ineffable cardinal AIM forcing Club Guessing Rock n' Roll S-Space PFA(S)[S] Singular cardinals combinatorics Respecting tree ccc Prevalent singular cardinals L-space Microscopic Approach Cohen real stationary hitting Square-Brackets Partition Relations Subtle tree property Cardinal function Sigma-Prikry Kurepa Hypothesis strongly bounded groups Commutative projection system Constructible Universe Forcing Axioms Ramsey theory over partitions Generalized Clubs Partition Relations Almost Souslin OCA Fast club very good scale Aronszajn tree Ulam matrix Subtle cardinal Commutative cancellative semigroups Sierpinski's onto mapping principle O-space Large Cardinals Absoluteness Postprocessing function Axiom R Dushnik-Miller Strong coloring Uniformly homogeneous Subadditive Hedetniemi's conjecture Shelah's Strong Hypothesis Chang's conjecture Reflecting stationary set polarized partition relation Jonsson cardinal Knaster weak Kurepa tree Successor of Regular Cardinal Cardinal Invariants Open Access stationary reflection reflection principles diamond star Almost countably chromatic Strongly compact cardinal Subnormal ideal Mandelbrot set Local Club Condensation. countably metacompact free Souslin tree specializable Souslin tree tensor product graph Diamond approachability ideal Parameterized proxy principle Small forcing
Author Archives: Assaf Rinot
Ramsey theory over partitions I: Positive Ramsey relations from forcing axioms
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, a correspondence between anti-Ramsey properties of partitions and chain conditions of the natural forcing notions … Continue reading
Posted in Partition Relations, Publications
Tagged 03E02, 03E17, 03E35, GMA, Martin's Axiom, positive partition relation, Ramsey theory over partitions
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A guessing principle from a Souslin tree, with applications to topology
Joint work with Roy Shalev. Abstract. We introduce a new combinatorial principle which we call $\clubsuit_{AD}$. This principle asserts the existence of a certain multi-ladder system with guessing and almost-disjointness features, and is shown to be sufficient for carrying out … Continue reading
Posted in Publications, Souslin Hypothesis, Topology
Tagged club_AD, Dowker space, O-space, regressive Souslin tree, S-Space, Souslin Tree, Vanishing levels
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MFO workshop in Set Theory, April 2020
The Set Theory workshop in Obwerwolfach was supposed to take place April 2020, but was transformed into a webinar, due to COVID-19. Here you will find the title, abstract, slides and video of my webinar talk. Talk Title: Transformations of … Continue reading
Posted in Invited Talks
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Transformations of the transfinite plane
Joint work with Jing Zhang. Abstract. We study the existence of transformations of the transfinite plane that allow one to reduce Ramsey-theoretic statements concerning uncountable Abelian groups into classical partition relations for uncountable cardinals. To exemplify: we prove that for every … Continue reading
Fake Reflection
Joint work with Gabriel Fernandes and Miguel Moreno. Abstract. We introduce a generalization of stationary set reflection which we call filter reflection, and show it is compatible with the axiom of constructibility as well as with strong forcing axioms. We … Continue reading
A microscopic approach to Souslin-tree constructions. Part II
Joint work with Ari Meir Brodsky. Abstract. In Part I of this series, we presented the microscopic approach to Souslin-tree constructions, and argued that all known $\diamondsuit$-based constructions of Souslin trees with various additional properties may be rendered as applications of … Continue reading
Sigma-Prikry forcing II: Iteration Scheme
Joint work with Alejandro Poveda and Dima Sinapova. Abstract. In Part I of this series, we introduced a class of notions of forcing which we call $\Sigma$-Prikry, and showed that many of the known Prikry-type notions of forcing that centers … Continue reading
Knaster and friends II: The C-sequence number
Joint work with Chris Lambie-Hanson. Abstract. Motivated by a characterization of weakly compact cardinals due to Todorcevic, we introduce a new cardinal characteristic, the C-sequence number, which can be seen as a measure of the compactness of a regular uncountable … Continue reading
The 15th International Workshop on Set Theory in Luminy, September 2019
I gave an invited talk at the 15th International Workshop on Set Theory in Luminy in Marseille, September 2019. Talk Title: Chain conditions, unbounded colorings and the C-sequence spectrum. Abstract: The productivity of the $\kappa$-chain condition, where $\kappa$ is a regular, … Continue reading
Posted in Invited Talks
Tagged Closed coloring, Knaster, Precaliber, stationary reflection, unbounded function
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Sigma-Prikry forcing I: The Axioms
Joint work with Alejandro Poveda and Dima Sinapova. Abstract. We introduce a class of notions of forcing which we call $\Sigma$-Prikry, and show that many of the known Prikry-type notions of forcing that centers around singular cardinals of countable cofinality … Continue reading
