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