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