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