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