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