Archives
Keywords
Rado's conjecture AIM forcing Amenable C-sequence L-space Analytic sets Prevalent singular cardinals Parameterized proxy principle Microscopic Approach Fat stationary set indecomposable ultrafilter Forcing Singular cofinality Open Access Fodor-type reflection strongly bounded groups Reflecting stationary set Subtle cardinal Successor of Regular Cardinal Greatly Mahlo Shelah's Strong Hypothesis Almost countably chromatic Club Guessing countably metacompact Iterated forcing Foundations Subadditive Prikry-type forcing Dushnik-Miller Erdos-Hajnal graphs Almost-disjoint family tensor product graph Distributive tree projective Boolean algebra Sigma-Prikry Jonsson cardinal Singular Density Ascent Path OCA Cardinal Invariants Coherent tree Knaster and friends Selective Ultrafilter Generalized Clubs Martin's Axiom Universal Sequences Hereditarily Lindelöf space Filter reflection Slim tree coloring number Kurepa Hypothesis polarized partition relation Diamond Non-saturation square regressive Souslin tree sap Poset 54G20 Successor of Singular Cardinal higher Baire space Uniformly coherent Sierpinski's onto mapping principle weak Kurepa tree weak square Forcing Axioms Hedetniemi's conjecture reflection principles Constructible Universe O-space Was Ulam right stationary reflection Postprocessing function HOD club_AD Minimal Walks middle diamond Diamond-sharp Large Cardinals Well-behaved magma Aronszajn tree C-sequence Local Club Condensation. Generalized descriptive set theory Luzin set Fast club Small forcing Ostaszewski square Hindman's Theorem Souslin Tree Commutative cancellative semigroups Precaliber Countryman line approachability ideal Uniformization free Souslin tree S-Space weak diamond Antichain Subtle tree property stationary hitting Respecting tree Cohen real Almost Souslin super-Souslin tree Strong coloring Strongly compact cardinal Diamond for trees square principles Ramsey theory over partitions Chang's conjecture free Boolean algebra Intersection model diamond star nonmeager set specializable Souslin tree Square-Brackets Partition Relations Mandelbrot set Rainbow sets full tree very good scale P-Ideal Dichotomy Absoluteness SNR Sakurai's Bell inequality Lipschitz reduction xbox ZFC construction Knaster Weakly compact cardinal Reduced Power Partition Relations Chromatic number Subnormal ideal stick unbounded function Cardinal function Ineffable cardinal Closed coloring Whitehead Problem Strongly Luzin set positive partition relation GMA Ulam matrix Axiom R Rock n' Roll incompactness Commutative projection system Erdos Cardinal Vanishing levels Dowker space transformations ccc b-scale PFA Nonspecial tree Uniformly homogeneous Singular cardinals combinatorics PFA(S)[S]
Tag Archives: Open Access
Full Souslin trees at small cardinals
Joint work with Shira Yadai and Zhixing You. Abstract. A $\kappa$-tree is full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full $\kappa$-Souslin tree may consistently exist. Shelah gave an affirmative … Continue reading
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
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
