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weak diamond Nonspecial tree Shelah's Strong Hypothesis Postprocessing function Absoluteness C-sequence Cardinal function Open Access Rock n' Roll Was Ulam right Forcing OCA Selective Ultrafilter Foundations Successor of Regular Cardinal Ramsey theory over partitions Lipschitz reduction S-Space club_AD Precaliber Souslin Tree reflection principles Almost-disjoint family unbounded function Fat stationary set polarized partition relation very good scale Large Cardinals Diamond for trees Ostaszewski square Universal Sequences full tree Sakurai's Bell inequality strongly bounded groups diamond star Diamond square free Souslin tree positive partition relation Analytic sets Hereditarily Lindelöf space Well-behaved magma Subadditive Subtle cardinal Fodor-type reflection tensor product graph Dushnik-Miller Reduced Power weak square Commutative projection system Minimal Walks weak Kurepa tree Cardinal Invariants Poset 54G20 GMA Uniformization Respecting tree higher Baire space O-space Kurepa Hypothesis approachability ideal stick Mandelbrot set Prikry-type forcing Diamond-sharp Chang's conjecture Knaster Distributive tree Ascent Path PFA(S)[S] Cohen real Countryman line Uniformly coherent Antichain Intersection model HOD stationary reflection Weakly compact cardinal Reflecting stationary set Fast club Martin's Axiom Constructible Universe Axiom R Chromatic number Ineffable cardinal Coherent tree Subnormal ideal Non-saturation specializable Souslin tree Commutative cancellative semigroups Luzin set Singular Density sap SNR P-Ideal Dichotomy Greatly Mahlo Vanishing levels Hedetniemi's conjecture transformations indecomposable ultrafilter Strongly Luzin set Strong coloring free Boolean algebra Successor of Singular Cardinal stationary hitting Jonsson cardinal Aronszajn tree Microscopic Approach regressive Souslin tree Subtle tree property Erdos-Hajnal graphs Whitehead Problem Local Club Condensation. Uniformly homogeneous incompactness Generalized Clubs Strongly compact cardinal Amenable C-sequence countably metacompact projective Boolean algebra Singular cofinality Small forcing Generalized descriptive set theory Singular cardinals combinatorics Sigma-Prikry Forcing Axioms Prevalent singular cardinals Parameterized proxy principle Knaster and friends ZFC construction xbox b-scale Filter reflection Dowker space Closed coloring nonmeager set Square-Brackets Partition Relations Rainbow sets Hindman's Theorem PFA square principles super-Souslin tree middle diamond AIM forcing Slim tree Club Guessing Ulam matrix Erdos Cardinal Almost Souslin Iterated forcing Sierpinski's onto mapping principle L-space Partition Relations Rado's conjecture ccc coloring number Almost countably chromatic
Tag Archives: Universal Sequences
Universal binary sequences
Notation. Write $\mathcal Q(A):=\{ a\subseteq A\mid a\text{ is finite}, a\neq\emptyset\}$. Suppose for the moment that we are given a fixed sequence $\langle f_\alpha:\omega\rightarrow2\mid \alpha\in a\rangle$, indexed by some set $a$ of ordinals. Then, for every function $h:a\rightarrow\omega$ and $i<\omega$, we … Continue reading
Syndetic colorings with applications to S and L
Notation. Write $\mathcal Q(A):=\{ a\subseteq A\mid a\text{ is finite}, a\neq\emptyset\}$. Definition. An L-space is a regular hereditarily Lindelöf topological space which is not hereditarily separable. Definition. We say that a coloring $c:[\omega_1]^2\rightarrow\omega$ is L-syndetic if the following holds. For every uncountable … Continue reading
