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Ramsey theory over partitions GMA free Souslin tree Antichain Forcing Axiom R Almost Souslin Microscopic Approach weak diamond Ascent Path HOD positive partition relation Singular cofinality countably metacompact Precaliber Dushnik-Miller SNR Postprocessing function Chang's conjecture Almost countably chromatic Strongly Luzin set polarized partition relation free Boolean algebra Subtle tree property Successor of Regular Cardinal Fodor-type reflection Subtle cardinal Minimal Walks Lipschitz reduction stick Local Club Condensation. Martin's Axiom middle diamond Kurepa Hypothesis unbounded function Club Guessing Diamond P-Ideal Dichotomy Foundations Chromatic number Shelah's Strong Hypothesis Strong coloring transformations Rado's conjecture very good scale Knaster and friends Hedetniemi's conjecture PFA(S)[S] Nonspecial tree Sakurai's Bell inequality Fat stationary set regressive Souslin tree Prikry-type forcing Singular Density club_AD Generalized descriptive set theory Square-Brackets Partition Relations AIM forcing Ulam matrix full tree square reflection principles higher Baire space Coherent tree Souslin Tree Large Cardinals incompactness Reflecting stationary set Well-behaved magma approachability ideal PFA S-Space Cardinal function Subadditive square principles Dowker space diamond star Rock n' Roll Iterated forcing Absoluteness Hindman's Theorem Analytic sets Non-saturation Distributive tree indecomposable ultrafilter Weakly compact cardinal Filter reflection weak Kurepa tree ZFC construction strongly bounded groups Slim tree Almost-disjoint family projective Boolean algebra Closed coloring Diamond for trees Generalized Clubs Reduced Power Jonsson cardinal Greatly Mahlo stationary reflection Subnormal ideal Luzin set Sigma-Prikry Aronszajn tree O-space 54G20 Vanishing levels Cohen real Forcing Axioms Open Access Erdos-Hajnal graphs Whitehead Problem Selective Ultrafilter Commutative cancellative semigroups Parameterized proxy principle sap Was Ulam right xbox stationary hitting Successor of Singular Cardinal super-Souslin tree nonmeager set Universal Sequences Erdos Cardinal Hereditarily Lindelöf space Constructible Universe ccc Ostaszewski square Uniformly homogeneous Diamond-sharp b-scale Knaster C-sequence Rainbow sets specializable Souslin tree Small forcing Amenable C-sequence OCA Partition Relations Ineffable cardinal Uniformly coherent coloring number weak square Poset Cardinal Invariants Mandelbrot set Prevalent singular cardinals Singular cardinals combinatorics Fast club Uniformization L-space Sierpinski's onto mapping principle tensor product graph
Tag Archives: 03E50
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