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