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Hedetniemi's conjecture coloring number Dowker space S-Space Forcing Axioms Antichain Chang's conjecture weak Kurepa tree Chromatic number Rado's conjecture Nonspecial tree P-Ideal Dichotomy Singular Density Almost Souslin Closed coloring super-Souslin tree Hindman's Theorem Commutative cancellative semigroups Amenable C-sequence Reflecting stationary set Ramsey theory over partitions Minimal Walks strongly bounded groups Subtle tree property Souslin Tree stationary reflection club_AD Erdos-Hajnal graphs Subadditive Strong coloring unbounded function Diamond-sharp countably metacompact stick Local Club Condensation. Strongly Luzin set Martin's Axiom HOD Mandelbrot set Diamond for trees Selective Ultrafilter Analytic sets Precaliber ZFC construction Lipschitz reduction Subnormal ideal weak diamond b-scale Weakly compact cardinal Greatly Mahlo Subtle cardinal L-space Sakurai's Bell inequality ccc regressive Souslin tree Open Access Aronszajn tree Singular cofinality PFA square OCA Constructible Universe Sierpinski's onto mapping principle xbox Uniformly homogeneous reflection principles indecomposable ultrafilter Luzin set tensor product graph Generalized Clubs Shelah's Strong Hypothesis Cardinal Invariants Fodor-type reflection Singular cardinals combinatorics Prevalent singular cardinals polarized partition relation Postprocessing function O-space diamond star square principles approachability ideal Knaster and friends sap Iterated forcing nonmeager set Generalized descriptive set theory Kurepa Hypothesis Axiom R middle diamond Square-Brackets Partition Relations Rock n' Roll Was Ulam right Ascent Path Rainbow sets weak square Parameterized proxy principle GMA Filter reflection Absoluteness Successor of Singular Cardinal Diamond specializable Souslin tree free Boolean algebra Dushnik-Miller Non-saturation Sigma-Prikry Almost countably chromatic Successor of Regular Cardinal SNR Ineffable cardinal Fast club Coherent tree 54G20 stationary hitting Well-behaved magma Cardinal function Uniformly coherent Club Guessing Knaster incompactness Fat stationary set Vanishing levels Hereditarily Lindelöf space Prikry-type forcing Small forcing Reduced Power Partition Relations very good scale Foundations Ulam matrix Slim tree C-sequence Microscopic Approach Almost-disjoint family Universal Sequences full tree PFA(S)[S] Large Cardinals higher Baire space Forcing free Souslin tree Erdos Cardinal AIM forcing Ostaszewski square Jonsson cardinal Uniformization Poset transformations positive partition relation projective Boolean algebra Distributive tree Whitehead Problem Cohen real
Tag Archives: stick
A new small Dowker space
Joint work with Roy Shalev and Stevo Todorcevic. Abstract. It is proved that if there exists a Luzin set, or if either the stick principle or $\diamondsuit(\mathfrak b)$ hold, then an instance of the guessing principle $\clubsuit_{AD}$ holds at the … Continue reading
Strongest transformations
Joint work with Jing Zhang. Abstract. We continue our study of maps transforming high-dimensional complicated objects into squares of stationary sets. Previously, we proved that many such transformations exist in ZFC, and here we address the consistency of the strongest … Continue reading
Posted in Partition Relations, Publications
Tagged Diamond, Minimal Walks, square, Square-Brackets Partition Relations, stick, transformations, xbox
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Polychromatic colorings
These are lectures notes of two talks Dani Livne gave in our Infinite Combinatorics seminar. I did not take notes in real-time, hence, all possible mistakes here are due to myself. Recall that a function $f:A\rightarrow B$ is said to … Continue reading