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