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