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