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Constructible Universe Diamond Successor of Singular Cardinal Subadditive Club Guessing Selective Ultrafilter Hereditarily Lindelöf space Sakurai's Bell inequality Ramsey theory over partitions Erdos Cardinal Uniformly homogeneous reflection principles Subnormal ideal Slim tree Singular cardinals combinatorics Small forcing nonmeager set ccc approachability ideal SNR Weakly compact cardinal Cardinal function Subtle tree property stick Prevalent singular cardinals free Boolean algebra Singular Density Local Club Condensation. Kurepa Hypothesis square Almost Souslin Singular cofinality Non-saturation Almost-disjoint family Uniformly coherent Fat stationary set Uniformization Cohen real P-Ideal Dichotomy Chang's conjecture Nonspecial tree Successor of Regular Cardinal Shelah's Strong Hypothesis Hindman's Theorem Distributive tree Fast club Was Ulam right? polarized partition relation Lipschitz reduction Sigma-Prikry Ostaszewski square Cardinal Invariants Square-Brackets Partition Relations Strong coloring OCA C-sequence GMA Erdos-Hajnal graphs sap Sierpinski's onto mapping principle Axiom R Knaster Coherent tree L-space Martin's Axiom tensor product graph Minimal Walks PFA(S)[S] Large Cardinals Closed coloring super-Souslin tree HOD 54G20 specializable Souslin tree Commutative projection system Jonsson cardinal unbounded function weak square strongly bounded groups weak Kurepa tree Reduced Power xbox Rado's conjecture Precaliber Diamond-sharp Rock n' Roll Postprocessing function regressive Souslin tree O-space incompactness Luzin set higher Baire space Souslin Tree Open Access Absoluteness Ulam matrix Strongly Luzin set Parameterized proxy principle Microscopic Approach Universal Sequences Chromatic number Generalized descriptive set theory Forcing weak diamond Aronszajn tree Foundations b-scale Filter reflection Respecting tree Intersection model Amenable C-sequence Dowker space Generalized Clubs Forcing Axioms Mandelbrot set Prikry-type forcing Rainbow sets square principles full tree free Souslin tree club_AD Hedetniemi's conjecture positive partition relation transformations Antichain indecomposable ultrafilter Knaster and friends middle diamond Greatly Mahlo Subtle cardinal ZFC construction Reflecting stationary set S-Space Almost countably chromatic projective Boolean algebra Well-behaved magma Countryman line Fodor-type reflection Poset Strongly compact cardinal very good scale PFA Iterated forcing countably metacompact stationary reflection Commutative cancellative semigroups Partition Relations Dushnik-Miller coloring number Ineffable cardinal Vanishing levels Whitehead Problem Diamond for trees Ascent Path stationary hitting diamond star AIM forcing Analytic sets
Tag Archives: Diamond for trees
120 Years of Choice, July 2024
I gave an invited talk at the 120 Years of Choice conference, July 2024. Talk Title: Mathematician’s best friend Abstract: Jensen’s diamond is a very useful postulate. It is well-known that it implies the continuum hypothesis, that it is equivalent … Continue reading
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 only guess the branches of a Kurepa tree. We demonstrate that this variation is considerably weaker than diamond by … Continue reading
Posted in Preprints, Squares and Diamonds
Tagged Diamond, Diamond for trees, Iterated forcing, Kurepa Hypothesis, weak Kurepa tree
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Full Souslin trees at small cardinals
Joint work with Shira Yadai and Zhixing You. Abstract. A
