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