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