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