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