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