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