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