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