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