### Archives

### Recent blog posts

- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Generalizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014

### Keywords

Rainbow sets Partition Relations Antichain Ascent Path Distributive tree S-Space Erdos-Hajnal graphs L-space Almost-disjoint famiy b-scale super-Souslin tree Constructible Universe approachability ideal tensor product graph HOD Non-saturation stationary hitting Microscopic Approach Coherent tree Singular cardinals combinatorics very good scale Prevalent singular cardinals P-Ideal Dichotomy free Boolean algebra Ostaszewski square Minimal Walks weak square 20M14 Souslin Tree Whitehead Problem Rock n' Roll ccc Reduced Power Selective Ultrafilter Club Guessing Cohen real xbox reflection principles Uniformization Axiom R Cardinal Invariants Hereditarily Lindelöf space Mandelbrot set Almost Souslin PFA(S)[S] Forcing Commutative cancellative semigroups Knaster Postprocessing function Singular Density Erdos Cardinal Large Cardinals Almost countably chromatic Absoluteness Hedetniemi's conjecture Martin's Axiom OCA Chromatic number Shelah's Strong Hypothesis PFA Uniformly coherent Nonspecial tree Hindman's Theorem 05A17 coloring number Cardinal function Singular coﬁnality Diamond incompactness Square-Brackets Partition Relations Poset Sakurai's Bell inequality Chang's conjecture Foundations polarized partition relation Successor of Regular Cardinal square principles Dushnik-Miller Luzin set Small forcing 11P99 Generalized Clubs Aronszajn tree Fodor-type reflection Forcing Axioms Prikry-type forcing diamond star Successor of Singular Cardinal Stevo Todorcevic stationary reflection Rado's conjecture middle diamond Jonsson cardinal Kurepa Hypothesis Slim tree Universal Sequences projective Boolean algebra Fat stationary set Parameterized proxy principle Weakly compact cardinal sap weak diamond square Fast club

# 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