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