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