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Nonspecial tree Knaster and friends xbox Generalized Clubs Entangled linear order Successor of Regular Cardinal Almost Souslin Filter reflection incompactness Rado's conjecture Absoluteness stick Strongly Luzin set L-space Dowker space Amenable C-sequence Analytic sets Ineffable cardinal square full tree club_AD Non-saturation Subtle tree property ccc Hereditarily Lindelöf space Almost-disjoint family free Boolean algebra Cohen real Slim tree Hedetniemi's conjecture Rainbow sets Sierpinski's onto mapping principle Commutative cancellative semigroups weak square Fat stationary set Coherent tree Diamond for trees Subadditive indecomposable filter Lipschitz reduction strongly bounded groups Well-behaved magma AIM forcing Ostaszewski square O-space Selective Ultrafilter Jonsson cardinal Mandelbrot set Constructible Universe Forcing with side conditions Small forcing Club Guessing HOD Greatly Mahlo Chang's conjecture polarized partition relation Fodor-type reflection weak diamond Sakurai's Bell inequality stationary hitting higher Baire space Shelah's Strong Hypothesis Ramsey theory over partitions Erdos-Hajnal graphs Ascending path C-sequence Uniformly coherent P-Ideal Dichotomy Square-Brackets Partition Relations Iterated forcing very good scale Ulam matrix Microscopic Approach middle diamond OCA Singular cardinals combinatorics Reduced Power square principles Partition relations for trees Uniformly homogeneous Diamond Kurepa Hypothesis reflection principles Foundations Weakly compact cardinal specializable Souslin tree Poset free Souslin tree Interval topology on trees weak Kurepa tree Fast club 54G20 Local Club Condensation. Distributive tree countably metacompact Singular Density Prevalent singular cardinals Whitehead Problem PFA(S)[S] Knaster Prikry-type forcing Dushnik-Miller Baumgartner's square Universal Sequences Successor of Singular Cardinal Countryman line SNR transformations Diamond-sharp b-scale tensor product graph Subtle cardinal Axiom R S-Space PFA Cardinal Invariants Ascent Path super-Souslin tree stationary reflection ZFC construction Reflecting stationary set Souslin Tree Sigma-Prikry Hindman's Theorem positive partition relation GMA perfectly normal Vanishing levels Large Cardinals Respecting tree Open Access Almost countably chromatic Rock n' Roll Monotonically far Luzin set Precaliber Forcing Antichain Postprocessing function Strong coloring Cardinal function Chromatic number Erdos Cardinal Uniformization diamond star Partition Relations regressive Souslin tree Was Ulam right? Subnormal ideal Intersection model approachability ideal Parameterized proxy principle Aronszajn tree Martin's Axiom Closed coloring Commutative projection system Minimal Walks Strongly compact cardinal projective Boolean algebra sap Singular cofinality unbounded function Generalized descriptive set theory coloring number Forcing Axioms nonmeager set
Tag Archives: Was Ulam right?
Conference in honor of Saharon Shelah’s 80th birthday
I gave an invited talk at the conference in honor of Shelah’s 80th birthday, July 2025. Talk Title: Marginalia to [Sh:365] Abstract: Solovay famously proved that every stationary subset of a regular uncountable cardinal kappa may be decomposed into kappa … Continue reading
Posted in Invited Talks
Tagged Greatly Mahlo, Strong coloring, Was Ulam right?
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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
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
