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Distributive tree Rock n' Roll Antichain Uniformly homogeneous Knaster and friends Respecting tree transformations unbounded function Cardinal function very good scale b-scale Ascending path Fast club Dushnik-Miller Cohen real Square-Brackets Partition Relations GMA square Amenable C-sequence Generalized Clubs AIM forcing incompactness Microscopic Approach projective Boolean algebra Slim tree Uniformization Shelah's Strong Hypothesis Chang's conjecture polarized partition relation approachability ideal Closed coloring Cardinal Invariants Prevalent singular cardinals stationary reflection Successor of Regular Cardinal Weakly compact cardinal tensor product graph super-Souslin tree Hindman's Theorem coloring number Iterated forcing Lipschitz reduction Ulam matrix Poset Fodor-type reflection Nonspecial tree Almost-disjoint family Non-saturation club_AD Erdos-Hajnal graphs Coherent tree weak square PFA L-space Monotonically far Subadditive Open Access Hereditarily Lindelöf space Sigma-Prikry Singular Density Singular cofinality Sakurai's Bell inequality square principles Hedetniemi's conjecture indecomposable filter xbox Partition relations for trees Diamond for trees Kurepa Hypothesis higher Baire space Large Cardinals Commutative cancellative semigroups Well-behaved magma ZFC construction countably metacompact Interval topology on trees PFA(S)[S] S-Space weak diamond Reduced Power 54G20 Uniformly coherent P-Ideal Dichotomy Minimal Walks Ascent Path Diamond-sharp Chromatic number O-space Ineffable cardinal Luzin set Analytic sets positive partition relation Forcing with side conditions stick Countryman line Whitehead Problem Martin's Axiom Generalized descriptive set theory Successor of Singular Cardinal C-sequence Dowker space Erdos Cardinal nonmeager set Axiom R Subtle tree property Foundations Commutative projection system Rainbow sets Constructible Universe full tree Universal Sequences reflection principles free Boolean algebra strongly bounded groups Forcing Selective Ultrafilter ccc Strongly Luzin set Intersection model Subtle cardinal Filter reflection Small forcing sap Vanishing levels Ostaszewski square Parameterized proxy principle Local Club Condensation. middle diamond Singular cardinals combinatorics SNR OCA Souslin Tree HOD weak Kurepa tree Almost Souslin Postprocessing function Sierpinski's onto mapping principle diamond star Partition Relations Strong coloring Precaliber Prikry-type forcing specializable Souslin tree Jonsson cardinal free Souslin tree Subnormal ideal Aronszajn tree Fat stationary set Reflecting stationary set perfectly normal Almost countably chromatic stationary hitting Knaster Forcing Axioms Was Ulam right? regressive Souslin tree Rado's conjecture Entangled linear order Diamond Ramsey theory over partitions Absoluteness Strongly compact cardinal Mandelbrot set Club Guessing Greatly Mahlo
Tag Archives: 03E35
Ketonen’s question and other cardinal sins
Joint work with Zhixing You and Jiachen Yuan. Abstract. Answering a question of Ketonen from the late 1970’s, it is proved that a weakly compact cardinal carrying an indecomposable ultrafilter need not be measurable. The result is obtained by analyzing … 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?
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Was Ulam right? I: Basic theory and subnormal ideals
Joint work with Tanmay Inamdar. Abstract. We introduce various coloring principles which generalize the so-called onto mapping principle of Sierpinski to larger cardinals and general ideals. We prove that these principles capture the notion of an Ulam matrix and allow … Continue reading
Ramsey theory over partitions III: Strongly Luzin sets and partition relations
Joint work with Menachem Kojman and Juris Steprāns. Abstract. The strongest type of coloring of pairs of countable ordinals, gotten by Todorcevic from a strongly Luzin set, is shown to be equivalent to the existence of a nonmeager set of … Continue reading
Ramsey theory over partitions I: Positive Ramsey relations from forcing axioms
Joint work with Menachem Kojman and Juris Steprāns. Abstract. In this series of papers, we advance Ramsey theory of colorings over partitions. In this part, a correspondence between anti-Ramsey properties of partitions and chain conditions of the natural forcing notions … Continue reading
Posted in Partition Relations, Publications
Tagged 03E02, 03E17, 03E35, GMA, Martin's Axiom, positive partition relation, Ramsey theory over partitions
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
Fake Reflection
Joint work with Gabriel Fernandes and Miguel Moreno. Abstract. We introduce a generalization of stationary set reflection which we call filter reflection, and show it is compatible with the axiom of constructibility as well as with strong forcing axioms. We … 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
A remark on Schimmerling’s question
Joint work with Ari Meir Brodsky. Abstract. Schimmerling asked whether $\square^*_\lambda$ together with GCH entails the existence of a $\lambda^+$-Souslin tree, for a singular cardinal $\lambda$. Here, we provide an affirmative answer under the additional assumption that there exists a … Continue reading
