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Ascent Path Singular cardinals combinatorics Small forcing projective Boolean algebra strongly bounded groups Postprocessing function Mandelbrot set Ulam matrix Ramsey theory over partitions Cardinal function Minimal Walks Luzin set Distributive tree nonmeager set Subtle tree property free Souslin tree Square-Brackets Partition Relations Non-saturation Diamond Cohen real Poset Diamond-sharp Martin's Axiom Rainbow sets Constructible Universe Dushnik-Miller positive partition relation Open Access Chromatic number Souslin Tree Aronszajn tree very good scale Uniformization Diamond for trees Fodor-type reflection Almost countably chromatic Shelah's Strong Hypothesis free Boolean algebra Coherent tree Singular Density Sierpinski's onto mapping principle Ineffable cardinal stick Almost-disjoint family P-Ideal Dichotomy O-space Knaster and friends Generalized Clubs HOD Fast club S-Space Nonspecial tree SNR Was Ulam right? Fat stationary set Sakurai's Bell inequality Iterated forcing GMA Greatly Mahlo incompactness sap Weakly compact cardinal Microscopic Approach Erdos Cardinal full tree ccc Forcing Hedetniemi's conjecture Vanishing levels Ostaszewski square Singular cofinality weak square Countryman line Subtle cardinal countably metacompact Whitehead Problem Prikry-type forcing Intersection model square Universal Sequences Jonsson cardinal Sigma-Prikry L-space diamond star Absoluteness Partition Relations Closed coloring Commutative cancellative semigroups Axiom R Filter reflection regressive Souslin tree Successor of Regular Cardinal Almost Souslin Well-behaved magma Reduced Power transformations b-scale Prevalent singular cardinals weak diamond AIM forcing Amenable C-sequence 54G20 Lipschitz reduction stationary hitting Foundations Dowker space square principles ZFC construction middle diamond Selective Ultrafilter Rock n' Roll Rado's conjecture Reflecting stationary set super-Souslin tree coloring number Local Club Condensation. Chang's conjecture Kurepa Hypothesis Knaster Uniformly coherent Hereditarily Lindelöf space Analytic sets reflection principles Strongly compact cardinal polarized partition relation Respecting tree C-sequence Cardinal Invariants tensor product graph stationary reflection club_AD specializable Souslin tree Slim tree indecomposable ultrafilter unbounded function Subnormal ideal Strong coloring Successor of Singular Cardinal Subadditive Forcing Axioms Erdos-Hajnal graphs Strongly Luzin set Uniformly homogeneous Generalized descriptive set theory Antichain xbox PFA(S)[S] Large Cardinals Hindman's Theorem OCA PFA Commutative projection system Precaliber higher Baire space Parameterized proxy principle weak Kurepa tree Club Guessing approachability ideal
Tag Archives: 03E35
Ketonen’s question and other cardinal sins
Joint work with Zhixing You and Jiachen Yuan. Abstract. Intersection models of generic extensions obtained from a commutative projection systems of notions of forcing has recently regained interest, especially in the study of descriptive set theory. Here, we show that … Continue reading
Posted in Compactness, Preprints
Tagged 03E05, 03E35, 03E55, Ascent Path, C-sequence, Commutative projection system, indecomposable ultrafilter, Intersection model, Strongly compact cardinal
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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, 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
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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
Weak square and stationary reflection
Joint work with Gunter Fuchs. Abstract. It is well-known that the square principle
Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E35, 03E57, Diamond, Forcing Axioms, stationary reflection, weak square
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