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