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Ramsey theory over partitions indecomposable filter P-Ideal Dichotomy Subnormal ideal Foundations higher Baire space Monotonically far Rock n' Roll Interval topology on trees Almost Souslin incompactness Forcing Prikry-type forcing Dowker space Antichain square transformations Erdos-Hajnal graphs square principles Cardinal function free Souslin tree Knaster Axiom R Sakurai's Bell inequality Whitehead Problem Subadditive b-scale Small forcing stick Vanishing levels Minimal Walks coloring number Iterated forcing Ascending path Local Club Condensation. Souslin Tree L-space Kurepa Hypothesis Knaster and friends PFA(S)[S] Partition relations for trees Fodor-type reflection Was Ulam right? Shelah's Strong Hypothesis Square-Brackets Partition Relations Generalized Clubs Absoluteness very good scale free Boolean algebra Subtle cardinal AIM forcing Uniformization Club Guessing Luzin set Sierpinski's onto mapping principle Almost countably chromatic Rainbow sets Fat stationary set Open Access O-space Diamond for trees Non-saturation Jonsson cardinal middle diamond Precaliber Successor of Singular Cardinal Successor of Regular Cardinal Singular Density sap Partition Relations Nonspecial tree Microscopic Approach GMA SNR positive partition relation Singular cardinals combinatorics xbox 54G20 S-Space Intersection model Cohen real Prevalent singular cardinals Filter reflection weak Kurepa tree club_AD Cardinal Invariants Commutative cancellative semigroups regressive Souslin tree Coherent tree diamond star Closed coloring strongly bounded groups Large Cardinals Lipschitz reduction polarized partition relation weak square Ulam matrix Forcing with side conditions Poset Mandelbrot set Forcing Axioms Constructible Universe Countryman line Sigma-Prikry Amenable C-sequence PFA perfectly normal specializable Souslin tree Uniformly coherent Chang's conjecture super-Souslin tree weak diamond OCA Weakly compact cardinal Strong coloring Hedetniemi's conjecture Generalized descriptive set theory Rado's conjecture Ineffable cardinal HOD Analytic sets ZFC construction Commutative projection system Fast club Subtle tree property projective Boolean algebra Distributive tree reflection principles Hereditarily Lindelöf space Respecting tree Selective Ultrafilter Erdos Cardinal countably metacompact Diamond-sharp stationary reflection Universal Sequences Postprocessing function full tree Slim tree Aronszajn tree Hindman's Theorem Parameterized proxy principle unbounded function nonmeager set Singular cofinality approachability ideal Ostaszewski square Entangled linear order Martin's Axiom Reduced Power Diamond C-sequence tensor product graph Well-behaved magma Greatly Mahlo Almost-disjoint family Ascent Path Chromatic number Strongly compact cardinal Dushnik-Miller ccc Reflecting stationary set Strongly Luzin set stationary hitting Uniformly homogeneous
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
