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Prevalent singular cardinals regressive Souslin tree weak diamond S-Space C-sequence Diamond for trees Minimal Walks free Boolean algebra Aronszajn tree P-Ideal Dichotomy Dowker space b-scale Cardinal Invariants weak Kurepa tree Luzin set strongly bounded groups Generalized descriptive set theory indecomposable ultrafilter Hindman's Theorem Foundations Souslin Tree Diamond-sharp Microscopic Approach Uniformly homogeneous Small forcing Strong coloring Singular cardinals combinatorics Mandelbrot set Large Cardinals Diamond specializable Souslin tree Lipschitz reduction Erdos-Hajnal graphs Antichain Fat stationary set Countryman line O-space Martin's Axiom Weakly compact cardinal Analytic sets Forcing Axioms Rainbow sets free Souslin tree countably metacompact PFA approachability ideal Sierpinski's onto mapping principle Sigma-Prikry transformations Slim tree Filter reflection Almost countably chromatic L-space nonmeager set Chromatic number polarized partition relation stationary hitting Shelah's Strong Hypothesis Knaster and friends Square-Brackets Partition Relations Distributive tree tensor product graph Cohen real Fodor-type reflection Commutative projection system Was Ulam right Rado's conjecture HOD Ineffable cardinal Knaster Intersection model Postprocessing function AIM forcing Dushnik-Miller Ascent Path Iterated forcing Closed coloring OCA 54G20 ccc Singular Density Almost Souslin Almost-disjoint family coloring number club_AD Subnormal ideal Universal Sequences ZFC construction Commutative cancellative semigroups sap unbounded function Chang's conjecture Nonspecial tree Forcing Uniformly coherent super-Souslin tree Whitehead Problem Non-saturation full tree Well-behaved magma Kurepa Hypothesis Subadditive Constructible Universe positive partition relation Fast club Club Guessing Respecting tree Hereditarily Lindelöf space Strongly Luzin set Uniformization square principles reflection principles Absoluteness middle diamond Rock n' Roll Coherent tree Local Club Condensation. SNR Reduced Power Selective Ultrafilter Ulam matrix incompactness Erdos Cardinal stick Subtle cardinal Subtle tree property Amenable C-sequence GMA Reflecting stationary set PFA(S)[S] Sakurai's Bell inequality very good scale Jonsson cardinal Poset projective Boolean algebra Generalized Clubs Prikry-type forcing stationary reflection weak square Hedetniemi's conjecture Axiom R Ramsey theory over partitions Vanishing levels Parameterized proxy principle Ostaszewski square square Successor of Singular Cardinal Successor of Regular Cardinal higher Baire space xbox Greatly Mahlo Precaliber Singular cofinality Cardinal function Open Access diamond star Strongly compact cardinal Partition Relations
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 $\kappa$-tree is full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full $\kappa$-Souslin tree may consistently exist. Shelah gave an affirmative … Continue reading
