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