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