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