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