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