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