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