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