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