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Axiom R b-scale Rado's conjecture weak Kurepa tree Minimal Walks Successor of Regular Cardinal projective Boolean algebra Slim tree Subadditive Fodor-type reflection square principles Analytic sets Fat stationary set club_AD Almost Souslin Local Club Condensation. Singular cardinals combinatorics Subtle cardinal Square-Brackets Partition Relations Souslin Tree Subtle tree property Selective Ultrafilter Sakurai's Bell inequality Diamond-sharp Universal Sequences Kurepa Hypothesis Chromatic number Closed coloring Foundations Commutative cancellative semigroups positive partition relation PFA Commutative projection system Diamond Diamond for trees Iterated forcing Ineffable cardinal weak diamond super-Souslin tree Vanishing levels Cardinal function C-sequence coloring number Antichain very good scale Absoluteness HOD Erdos Cardinal stick S-Space Amenable C-sequence Ramsey theory over partitions Poset Microscopic Approach Club Guessing Small forcing Uniformly homogeneous Open Access Non-saturation Reduced Power higher Baire space Almost countably chromatic Hindman's Theorem Lipschitz reduction AIM forcing countably metacompact Hereditarily Lindelöf space PFA(S)[S] free Souslin tree Ulam matrix Reflecting stationary set xbox Luzin set regressive Souslin tree Prevalent singular cardinals Rock n' Roll strongly bounded groups Greatly Mahlo Ostaszewski square square Successor of Singular Cardinal Weakly compact cardinal Sierpinski's onto mapping principle full tree O-space unbounded function middle diamond Rainbow sets Cohen real Postprocessing function Shelah's Strong Hypothesis Distributive tree Almost-disjoint family Chang's conjecture Uniformly coherent Subnormal ideal Aronszajn tree 54G20 Fast club Singular cofinality Constructible Universe Partition Relations diamond star Dushnik-Miller stationary hitting tensor product graph Martin's Axiom free Boolean algebra Dowker space Strong coloring L-space GMA Hedetniemi's conjecture Erdos-Hajnal graphs Nonspecial tree Filter reflection Forcing Jonsson cardinal Well-behaved magma indecomposable ultrafilter Coherent tree Was Ulam right? nonmeager set ccc Uniformization reflection principles P-Ideal Dichotomy Ascent Path Large Cardinals OCA Knaster and friends incompactness Singular Density Generalized descriptive set theory SNR Whitehead Problem stationary reflection Sigma-Prikry Precaliber Respecting tree ZFC construction Intersection model sap Cardinal Invariants Forcing Axioms weak square Countryman line Strongly compact cardinal specializable Souslin tree Parameterized proxy principle Generalized Clubs Prikry-type forcing polarized partition relation Mandelbrot set Strongly Luzin set approachability ideal transformations Knaster
Tag Archives: Ulam matrix
Gdańsk Logic Conference, May 2023
I gave an invited talk at the first Gdańsk Logic Conference, May 2023. Talk Title: Was Ulam right? Abstract: An Ulam matrix is one of the earliest gems of infinite combinatorics. Around the same time of its discovery, another Polish … Continue reading
Winter School in Abstract Analysis, January 2023
I gave a 3-lecture tutorial at the Winter School in Abstract Analysis in Steken, January 2023. Title: Club guessing Abstract. Club guessing principles were introduced by Shelah as a weakening of Jensen’s diamond. Most spectacularly, they were used to prove … 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, 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
Partitioning a reflecting stationary set
Joint work with Maxwell Levine. Abstract. We address the question of whether a reflecting stationary set may be partitioned into two or more reflecting stationary subsets, providing various affirmative answers in ZFC. As an application to singular cardinals combinatorics, we infer … Continue reading
4th Arctic Set Theory Workshop, January 2019
I gave an invited talk at the Arctic Set Theory Workshop 4 in Kilpisjärvi, January 2019. Talk Title: Splitting a stationary set: Is there another way? Abstract: Motivated by a problem in pcf theory, we seek for a new way … Continue reading
Posted in Invited Talks
Tagged Club Guessing, Reflecting stationary set, Ulam matrix, very good scale
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