Archives
Keywords
square principles countably metacompact Uniformization Aronszajn tree Axiom R Generalized Clubs Cardinal function Cohen real club_AD nonmeager set reflection principles Whitehead Problem weak diamond Hedetniemi's conjecture Luzin set Postprocessing function Commutative cancellative semigroups Erdos Cardinal Ineffable cardinal Prikry-type forcing Ascending path HOD Vanishing levels Subtle tree property Large Cardinals Open Access stationary reflection Forcing Axioms Antichain Fodor-type reflection Precaliber Minimal Walks Respecting tree ZFC construction Square-Brackets Partition Relations Entangled linear order Reduced Power middle diamond Ostaszewski square Was Ulam right? Slim tree polarized partition relation Analytic sets Subtle cardinal Generalized descriptive set theory Almost countably chromatic P-Ideal Dichotomy Fat stationary set projective Boolean algebra Closed coloring Shelah's Strong Hypothesis full tree Greatly Mahlo Jonsson cardinal Erdos-Hajnal graphs Selective Ultrafilter Commutative projection system GMA Strong coloring Successor of Regular Cardinal Partition relations for trees Singular Density free Boolean algebra PFA(S)[S] Ulam matrix Strongly compact cardinal Knaster and friends Ramsey theory over partitions b-scale 54G20 Iterated forcing Cardinal Invariants Reflecting stationary set SNR Weakly compact cardinal tensor product graph square Uniformly homogeneous Small forcing ccc Rado's conjecture OCA Singular cardinals combinatorics free Souslin tree Uniformly coherent PFA Filter reflection perfectly normal Distributive tree Diamond C-sequence diamond star Constructible Universe Dushnik-Miller Sakurai's Bell inequality Club Guessing weak square sap Strongly Luzin set stick weak Kurepa tree Rock n' Roll Diamond-sharp Souslin Tree Absoluteness Diamond for trees transformations Chang's conjecture Ascent Path Rainbow sets Sigma-Prikry Hereditarily Lindelöf space Parameterized proxy principle very good scale unbounded function Well-behaved magma Universal Sequences regressive Souslin tree Sierpinski's onto mapping principle Successor of Singular Cardinal indecomposable filter Almost Souslin incompactness Chromatic number Coherent tree Forcing coloring number positive partition relation Almost-disjoint family specializable Souslin tree Hindman's Theorem approachability ideal Knaster Foundations Lipschitz reduction Prevalent singular cardinals strongly bounded groups stationary hitting Amenable C-sequence Subadditive Singular cofinality Fast club Non-saturation Dowker space xbox Partition Relations Interval topology on trees Poset O-space Subnormal ideal Forcing with side conditions Nonspecial tree higher Baire space S-Space Intersection model Martin's Axiom L-space Microscopic Approach AIM forcing Monotonically far Local Club Condensation. Mandelbrot set super-Souslin tree Countryman line Kurepa Hypothesis
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?
Comments Off on Conference in honor of Saharon Shelah’s 80th birthday
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
