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Shelah's Strong Hypothesis Rainbow sets very good scale Hedetniemi's conjecture Interval topology on trees strongly bounded groups ccc Coherent tree Reflecting stationary set Fodor-type reflection Square-Brackets Partition Relations sap Knaster and friends Universal Sequences square SNR approachability ideal coloring number Subadditive Jonsson cardinal middle diamond Almost Souslin Mandelbrot set Strong coloring Entangled linear order Uniformly homogeneous Intersection model weak square regressive Souslin tree Sigma-Prikry weak Kurepa tree Ramsey theory over partitions OCA Selective Ultrafilter Absoluteness L-space Ostaszewski square Diamond-sharp Prikry-type forcing countably metacompact Reduced Power incompactness Sierpinski's onto mapping principle Microscopic Approach Respecting tree diamond star Amenable C-sequence transformations AIM forcing Sakurai's Bell inequality Hindman's Theorem Partition relations for trees Club Guessing Vanishing levels Large Cardinals Aronszajn tree Whitehead Problem Erdos-Hajnal graphs Ascent Path Cohen real Ascending path perfectly normal Distributive tree stationary hitting HOD Diamond for trees PFA(S)[S] Almost-disjoint family Subtle cardinal Strongly compact cardinal ZFC construction Open Access S-Space Rock n' Roll tensor product graph Uniformly coherent Nonspecial tree Prevalent singular cardinals Subtle tree property indecomposable filter Dowker space projective Boolean algebra Generalized descriptive set theory Souslin Tree Foundations Precaliber xbox Non-saturation Antichain Well-behaved magma Uniformization club_AD Monotonically far polarized partition relation 54G20 Partition Relations Countryman line Erdos Cardinal Knaster Fast club Commutative cancellative semigroups Parameterized proxy principle stationary reflection positive partition relation Subnormal ideal Successor of Singular Cardinal weak diamond Closed coloring Cardinal Invariants Greatly Mahlo Minimal Walks Axiom R Constructible Universe Local Club Condensation. Chang's conjecture Forcing Axioms Lipschitz reduction Singular cofinality Successor of Regular Cardinal Rado's conjecture full tree GMA Singular cardinals combinatorics Filter reflection Poset Singular Density Chromatic number Forcing with side conditions Hereditarily Lindelöf space Commutative projection system Slim tree Cardinal function Fat stationary set Generalized Clubs Forcing square principles Analytic sets Was Ulam right? Almost countably chromatic super-Souslin tree P-Ideal Dichotomy Small forcing Postprocessing function Luzin set Ulam matrix PFA C-sequence reflection principles specializable Souslin tree Ineffable cardinal Kurepa Hypothesis free Souslin tree free Boolean algebra higher Baire space Martin's Axiom unbounded function Iterated forcing b-scale nonmeager set stick Strongly Luzin set Dushnik-Miller O-space Diamond Weakly compact cardinal
Tag Archives: Greatly Mahlo
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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Full Souslin trees at small cardinals
Joint work with Shira Yadai and Zhixing You. Abstract. A $\kappa$-tree is full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full $\kappa$-Souslin tree may consistently exist. Shelah gave an affirmative … Continue reading
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
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
