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Ascent Path Selective Ultrafilter Partition Relations Ineffable cardinal Weakly compact cardinal tensor product graph Well-behaved magma sap O-space countably metacompact strongly bounded groups PFA Subadditive Nonspecial tree weak diamond Uniformization Intersection model Fodor-type reflection Vanishing levels super-Souslin tree Minimal Walks Local Club Condensation. Poset ZFC construction Forcing Prikry-type forcing Rock n' Roll Greatly Mahlo Ulam matrix C-sequence GMA regressive Souslin tree Generalized descriptive set theory Dushnik-Miller Almost Souslin Luzin set Jonsson cardinal Commutative projection system full tree diamond star P-Ideal Dichotomy reflection principles polarized partition relation Successor of Singular Cardinal Axiom R HOD Rado's conjecture Ramsey theory over partitions Almost-disjoint family Hindman's Theorem Fast club stationary hitting very good scale Chang's conjecture Subnormal ideal specializable Souslin tree weak Kurepa tree Uniformly coherent Diamond Postprocessing function Generalized Clubs Amenable C-sequence Filter reflection Coherent tree 54G20 club_AD Constructible Universe b-scale S-Space positive partition relation Mandelbrot set stick Iterated forcing Knaster and friends Hedetniemi's conjecture Absoluteness coloring number Strong coloring OCA free Souslin tree Foundations middle diamond Strongly compact cardinal Shelah's Strong Hypothesis stationary reflection Parameterized proxy principle Dowker space incompactness xbox free Boolean algebra unbounded function Reduced Power Distributive tree Fat stationary set ccc Club Guessing Martin's Axiom indecomposable filter Singular cofinality Uniformly homogeneous Successor of Regular Cardinal L-space Slim tree Cardinal function Knaster Sakurai's Bell inequality Souslin Tree approachability ideal Strongly Luzin set Whitehead Problem Hereditarily Lindelöf space SNR Diamond for trees Antichain Lipschitz reduction Countryman line Singular cardinals combinatorics transformations AIM forcing Large Cardinals Prevalent singular cardinals Diamond-sharp Aronszajn tree Subtle tree property Erdos-Hajnal graphs Rainbow sets Analytic sets Forcing Axioms weak square square principles higher Baire space Was Ulam right? Small forcing Open Access Chromatic number Reflecting stationary set Non-saturation Commutative cancellative semigroups Square-Brackets Partition Relations Microscopic Approach nonmeager set Kurepa Hypothesis Ostaszewski square Cardinal Invariants Respecting tree Cohen real Universal Sequences Sigma-Prikry Precaliber projective Boolean algebra Subtle cardinal Singular Density square Erdos Cardinal Sierpinski's onto mapping principle Closed coloring Almost countably chromatic PFA(S)[S]
Author Archives: Assaf Rinot
Strongest transformations
Joint work with Jing Zhang. Abstract. We continue our study of maps transforming high-dimensional complicated objects into squares of stationary sets. Previously, we proved that many such transformations exist in ZFC, and here we address the consistency of the strongest … Continue reading
Posted in Partition Relations, Publications
Tagged Diamond, Minimal Walks, square, Square-Brackets Partition Relations, stick, transformations, xbox
2 Comments
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
Posted in Publications, Souslin Hypothesis
Tagged Cardinal Invariants, Cohen real, nonmeager set
1 Comment
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
1 Comment
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
Posted in Publications, Souslin Hypothesis, Topology
Tagged club_AD, Dowker space, O-space, regressive Souslin tree, S-Space, Souslin Tree, Vanishing levels
2 Comments
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
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
