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