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