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