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Strongly compact cardinal club_AD middle diamond Luzin set Aronszajn tree stick Ramsey theory over partitions Small forcing Strongly Luzin set Sierpinski's onto mapping principle Selective Ultrafilter Non-saturation indecomposable filter Generalized Clubs sap Antichain Interval topology on trees Countryman line Forcing with side conditions HOD Almost countably chromatic Iterated forcing Uniformization regressive Souslin tree b-scale Intersection model Kurepa Hypothesis Rock n' Roll Closed coloring PFA Fast club stationary reflection perfectly normal Cardinal function Chromatic number Slim tree Club Guessing GMA Whitehead Problem Commutative projection system Hindman's Theorem Uniformly homogeneous free Boolean algebra full tree PFA(S)[S] Square-Brackets Partition Relations positive partition relation Subadditive Fodor-type reflection weak Kurepa tree Erdos-Hajnal graphs Cohen real free Souslin tree AIM forcing approachability ideal projective Boolean algebra Forcing Minimal Walks unbounded function Dushnik-Miller Strong coloring Shelah's Strong Hypothesis square Axiom R countably metacompact Local Club Condensation. Monotonically far xbox Jonsson cardinal Ostaszewski square Erdos Cardinal Dowker space Subnormal ideal incompactness Fat stationary set Ascending path specializable Souslin tree O-space Reflecting stationary set Souslin Tree ZFC construction Singular cardinals combinatorics Absoluteness stationary hitting Diamond Sakurai's Bell inequality 54G20 Was Ulam right? Singular cofinality Generalized descriptive set theory Nonspecial tree Knaster and friends Vanishing levels Greatly Mahlo strongly bounded groups Mandelbrot set Martin's Axiom Respecting tree Ineffable cardinal Partition relations for trees Universal Sequences Successor of Regular Cardinal Baumgartner's square square principles Postprocessing function Well-behaved magma Microscopic Approach Constructible Universe Ascent Path Successor of Singular Cardinal Almost Souslin Knaster Open Access Amenable C-sequence OCA P-Ideal Dichotomy Distributive tree Diamond-sharp tensor product graph Analytic sets Cardinal Invariants Poset Foundations polarized partition relation Uniformly coherent Entangled linear order coloring number weak diamond Weakly compact cardinal Rado's conjecture Subtle tree property SNR higher Baire space Reduced Power Sigma-Prikry nonmeager set Prikry-type forcing Partition Relations Diamond for trees Lipschitz reduction L-space S-Space Hedetniemi's conjecture C-sequence Coherent tree very good scale transformations Precaliber Parameterized proxy principle Prevalent singular cardinals super-Souslin tree Subtle cardinal Almost-disjoint family ccc Filter reflection Singular Density weak square Forcing Axioms reflection principles Hereditarily Lindelöf space Large Cardinals Commutative cancellative semigroups Rainbow sets Chang's conjecture Ulam matrix diamond star
Tag Archives: Open Access
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, Kurepa Hypothesis, Open Access, Subnormal ideal, Ulam matrix, Was Ulam right?
2 Comments
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 $\theta < \kappa$, the existence … Continue reading
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 $\Sigma$-Prikry, and show that many of the known Prikry-type notions of forcing that centers around singular cardinals of countable cofinality … Continue reading
Higher Souslin trees and the GCH, revisited
Abstract. It is proved that for every uncountable cardinal $\lambda$, GCH+$\square(\lambda^+)$ entails the existence of a $\text{cf}(\lambda)$-complete $\lambda^+$-Souslin tree. In particular, if GCH holds and there are no $\aleph_2$-Souslin trees, then $\aleph_2$ is weakly compact in Godel’s constructible universe, improving … Continue reading
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, Open Access, regressive Souslin tree, Souslin Tree, square, Weakly compact cardinal, xbox
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Reduced powers of Souslin trees
Joint work with Ari Meir Brodsky. Abstract. We study the relationship between a $\kappa$-Souslin tree $T$ and its reduced powers $T^\theta/\mathcal U$. Previous works addressed this problem from the viewpoint of a single power $\theta$, whereas here, tools are developed … Continue reading
Complicated colorings
Abstract. If $\lambda,\kappa$ are regular cardinals, $\lambda>\kappa^+$, and $E^\lambda_{\ge\kappa}$ admits a nonreflecting stationary set, then $\text{Pr}_1(\lambda,\lambda,\lambda,\kappa)$ holds. (Recall that $\text{Pr}_1(\lambda,\lambda,\lambda,\kappa)$ asserts the existence of a coloring $d:[\lambda]^2\rightarrow\lambda$ such that for any family $\mathcal A\subseteq[\lambda]^{<\kappa}$ of size $\lambda$, consisting of pairwise … Continue reading
Posted in Partition Relations, Publications
Tagged Minimal Walks, Open Access, Square-Brackets Partition Relations
2 Comments
