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