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Diamond-sharp Reflecting stationary set O-space Rado's conjecture AIM forcing regressive Souslin tree Forcing Axioms Erdos-Hajnal graphs L-space Reduced Power Postprocessing function diamond star Uniformization xbox Well-behaved magma square Forcing with side conditions Nonspecial tree Intersection model Whitehead Problem Antichain strongly bounded groups club_AD Ascent Path Microscopic Approach Almost Souslin Ascending path Almost-disjoint family Lipschitz reduction tensor product graph Strongly Luzin set Minimal Walks Large Cardinals 54G20 Cardinal Invariants perfectly normal polarized partition relation Small forcing full tree Cardinal function Successor of Regular Cardinal GMA Martin's Axiom Sierpinski's onto mapping principle Forcing Parameterized proxy principle b-scale very good scale indecomposable filter Vanishing levels sap Foundations projective Boolean algebra higher Baire space Partition relations for trees HOD transformations Ramsey theory over partitions Jonsson cardinal Shelah's Strong Hypothesis Fast club Monotonically far Commutative cancellative semigroups Mandelbrot set OCA Aronszajn tree S-Space Axiom R middle diamond free Boolean algebra Absoluteness Cohen real Amenable C-sequence Subnormal ideal Prevalent singular cardinals Kurepa Hypothesis Uniformly homogeneous Knaster Coherent tree Uniformly coherent Universal Sequences Slim tree Iterated forcing PFA(S)[S] Almost countably chromatic stick Hindman's Theorem Subadditive Subtle cardinal Prikry-type forcing countably metacompact Precaliber Souslin Tree Ulam matrix Strongly compact cardinal Rock n' Roll weak square Singular cofinality Entangled linear order weak diamond Ineffable cardinal Greatly Mahlo Successor of Singular Cardinal super-Souslin tree Distributive tree Local Club Condensation. stationary reflection Sigma-Prikry Diamond Generalized descriptive set theory Chromatic number Closed coloring ccc reflection principles coloring number Filter reflection Selective Ultrafilter Singular cardinals combinatorics nonmeager set Sakurai's Bell inequality Commutative projection system Countryman line PFA Ostaszewski square Non-saturation P-Ideal Dichotomy Luzin set Strong coloring Rainbow sets Hedetniemi's conjecture positive partition relation unbounded function Generalized Clubs stationary hitting Partition Relations Analytic sets Club Guessing Chang's conjecture Knaster and friends ZFC construction Square-Brackets Partition Relations Poset Interval topology on trees Diamond for trees Fodor-type reflection Subtle tree property approachability ideal weak Kurepa tree Was Ulam right? Weakly compact cardinal Respecting tree incompactness Singular Density Open Access free Souslin tree specializable Souslin tree SNR Dowker space Hereditarily Lindelöf space Fat stationary set C-sequence square principles Erdos Cardinal Constructible Universe Dushnik-Miller
Tag Archives: Non-saturation
Was Ulam right? III: Indecomposable ideals
Joint work with Tanmay Inamdar. Abstract. We continue our study of Ulam’s measure problem. In contrast to our previous works, we shift our focus from measures stratified by their additivity, to measures stratified by their indecomposability. The breakthrough here is … Continue reading
Jensen’s diamond principle and its relatives
This is chapter 6 in the book Set Theory and Its Applications (ISBN: 0821848127). Abstract: We survey some recent results on the validity of Jensen’s diamond principle at successor cardinals. We also discuss weakening of this principle such as club … Continue reading
A relative of the approachability ideal, diamond and non-saturation
Abstract: Let $\lambda$ denote a singular cardinal. Zeman, improving a previous result of Shelah, proved that $\square^*_\lambda$ together with $2^\lambda=\lambda^+$ implies $\diamondsuit_S$ for every $S\subseteq\lambda^+$ that reflects stationarily often. In this paper, for a subset $S\subset\lambda^+$, a normal subideal of … Continue reading
On guessing generalized clubs at the successors of regulars
Abstract: Konig, Larson and Yoshinobu initiated the study of principles for guessing generalized clubs, and introduced a construction of an higher Souslin tree from the strong guessing principle. Complementary to the author’s work on the validity of diamond and non-saturation … Continue reading
