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Jonsson cardinal middle diamond Reduced Power stationary hitting Almost countably chromatic Axiom R Weakly compact cardinal club_AD Generalized descriptive set theory Sakurai's Bell inequality indecomposable filter sap Prikry-type forcing Non-saturation P-Ideal Dichotomy GMA Vanishing levels AIM forcing Parameterized proxy principle Souslin Tree Uniformly coherent Poset xbox Erdos-Hajnal graphs tensor product graph Slim tree stationary reflection O-space Forcing Axioms Successor of Singular Cardinal incompactness Small forcing Ulam matrix Nonspecial tree Dowker space Selective Ultrafilter Analytic sets Rado's conjecture C-sequence Ostaszewski square higher Baire space Dushnik-Miller Kurepa Hypothesis Filter reflection Was Ulam right? Forcing with side conditions nonmeager set perfectly normal Square-Brackets Partition Relations PFA regressive Souslin tree Diamond unbounded function Fast club free Boolean algebra super-Souslin tree Ascending path Cardinal Invariants projective Boolean algebra Commutative cancellative semigroups Distributive tree Subadditive Fat stationary set Ineffable cardinal Martin's Axiom Subtle tree property Entangled linear order Partition Relations diamond star Partition relations for trees Sigma-Prikry Generalized Clubs Universal Sequences Whitehead Problem Subtle cardinal Coherent tree Foundations very good scale Amenable C-sequence Countryman line Knaster and friends coloring number full tree Chang's conjecture polarized partition relation Rock n' Roll Mandelbrot set Minimal Walks ccc Cohen real Strongly compact cardinal weak Kurepa tree weak square Absoluteness Microscopic Approach Ascent Path Club Guessing strongly bounded groups Fodor-type reflection specializable Souslin tree reflection principles stick Luzin set weak diamond Ramsey theory over partitions OCA free Souslin tree Shelah's Strong Hypothesis Hindman's Theorem HOD L-space Greatly Mahlo Singular Density PFA(S)[S] SNR Monotonically far Hereditarily Lindelöf space Open Access Strongly Luzin set positive partition relation approachability ideal Lipschitz reduction Aronszajn tree Commutative projection system Uniformization Subnormal ideal Singular cardinals combinatorics Prevalent singular cardinals Almost Souslin Respecting tree square Rainbow sets Singular cofinality Local Club Condensation. Iterated forcing Diamond-sharp ZFC construction Closed coloring countably metacompact Erdos Cardinal Well-behaved magma Uniformly homogeneous Almost-disjoint family b-scale Forcing 54G20 square principles Knaster Intersection model Successor of Regular Cardinal Chromatic number Large Cardinals Antichain Interval topology on trees Hedetniemi's conjecture Constructible Universe Cardinal function Sierpinski's onto mapping principle Reflecting stationary set Postprocessing function Precaliber S-Space transformations Strong coloring Diamond for trees
Author Archives: Assaf Rinot
On the ideal J[kappa]
Abstract. Motivated by a question from a recent paper by Gilton, Levine and Stejskalova, we obtain a new characterization of the ideal $J[\kappa]$, from which we confirm that $\kappa$-Souslin trees exist in various models of interest. As a corollary we … Continue reading
Posted in Publications, Souslin Hypothesis
Tagged Cardinal Invariants, Cohen real, nonmeager set
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Ramsey theory over partitions III: Strongly Luzin sets and partition relations
Joint work with Menachem Kojman and Juris Steprāns. Abstract. The strongest type of coloring of pairs of countable ordinals, gotten by Todorcevic from a strongly Luzin set, is shown to be equivalent to the existence of a nonmeager set of … Continue reading
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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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
Comments Off on MFO workshop in Set Theory, April 2020
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
