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S-Space Distributive tree 54G20 Hereditarily Lindelöf space Subtle tree property Shelah's Strong Hypothesis Generalized Clubs weak diamond Ulam matrix Successor of Singular Cardinal Countryman line Subadditive Fodor-type reflection Subnormal ideal Almost Souslin transformations Almost-disjoint family Cardinal function Poset stick Was Ulam right? Commutative cancellative semigroups Iterated forcing specializable Souslin tree ccc regressive Souslin tree square principles Forcing ZFC construction tensor product graph Non-saturation Fat stationary set stationary hitting Square-Brackets Partition Relations Hindman's Theorem Diamond for trees Subtle cardinal Postprocessing function Singular Density Generalized descriptive set theory free Boolean algebra Open Access Ostaszewski square approachability ideal Sierpinski's onto mapping principle Greatly Mahlo Uniformly coherent Absoluteness Parameterized proxy principle Rainbow sets Hedetniemi's conjecture O-space L-space Almost countably chromatic Diamond-sharp b-scale Fast club Intersection model AIM forcing Jonsson cardinal Large Cardinals positive partition relation super-Souslin tree stationary reflection Universal Sequences Reduced Power SNR Ineffable cardinal square Antichain Respecting tree xbox Strongly compact cardinal full tree Amenable C-sequence Chang's conjecture Local Club Condensation. Uniformization Foundations Filter reflection P-Ideal Dichotomy Closed coloring PFA(S)[S] Lipschitz reduction Erdos Cardinal sap PFA HOD weak square Weakly compact cardinal Dowker space Selective Ultrafilter diamond star Prikry-type forcing Uniformly homogeneous Sakurai's Bell inequality Kurepa Hypothesis nonmeager set Coherent tree Chromatic number free Souslin tree Singular cardinals combinatorics C-sequence unbounded function Martin's Axiom Minimal Walks Rado's conjecture Erdos-Hajnal graphs higher Baire space Ramsey theory over partitions Club Guessing Rock n' Roll Mandelbrot set Knaster Successor of Regular Cardinal GMA countably metacompact Slim tree coloring number Souslin Tree Ascent Path Whitehead Problem incompactness projective Boolean algebra middle diamond Aronszajn tree Small forcing Sigma-Prikry Cohen real Nonspecial tree weak Kurepa tree Strongly Luzin set Knaster and friends Partition Relations Well-behaved magma Reflecting stationary set club_AD Axiom R Singular cofinality Vanishing levels Dushnik-Miller Cardinal Invariants polarized partition relation OCA Strong coloring Diamond Microscopic Approach strongly bounded groups Precaliber Forcing Axioms Constructible Universe Prevalent singular cardinals reflection principles Luzin set indecomposable ultrafilter very good scale Commutative projection system Analytic sets
Tag Archives: Open Access
Full Souslin trees at small cardinals
Joint work with Shira Yadai and Zhixing You. Abstract. A
Sums of triples in Abelian groups
Joint work with Ido Feldman. Abstract. Motivated by a problem in additive Ramsey theory, we extend Todorcevic’s partitions of three-dimensional combinatorial cubes to handle additional three-dimensional objects. As a corollary, we get that if the continuum hypothesis fails, then for … Continue reading
A club guessing toolbox I
Joint work with Tanmay Inamdar. Abstract. Club guessing principles were introduced by Shelah as a weakening of Jensen’s diamond. Most spectacularly, they were used to prove Shelah’s ZFC bound on the power of the first singular cardinal. These principles have … Continue reading
Was Ulam right? II: Small width and general ideals
Joint work with Tanmay Inamdar. Abstract. We continue our study of Sierpinski-type colourings. In contrast to the prequel paper, we focus here on colourings for ideals stratified by their completeness degree. In particular, improving upon Ulam’s theorem and its extension … Continue reading
Posted in Partition Relations, Publications
Tagged 03E02, 03E35, 03E55, C-sequence, Open Access, Subnormal ideal, Ulam matrix, Was Ulam right?
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Knaster and friends III: Subadditive colorings
Joint work with Chris Lambie-Hanson. Abstract. We continue our study of strongly unbounded colorings, this time focusing on subadditive maps. In Part I of this series, we showed that, for many pairs of infinite cardinals
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
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
Higher Souslin trees and the GCH, revisited
Abstract. It is proved that for every uncountable cardinal
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, Open Access, regressive Souslin tree, Souslin Tree, square, Weakly compact cardinal, xbox
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