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