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