### 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

PFA Successor of Singular Cardinal Commutative cancellative semigroups Ostaszewski square Hindman's Theorem Shelah's Strong Hypothesis Almost-disjoint famiy Prevalent singular cardinals Successor of Regular Cardinal 20M14 Generalized Clubs Uniformly coherent ccc Chang's conjecture Singular Density weak square Absoluteness Minimal Walks Cardinal Invariants diamond star square principles Sakurai's Bell inequality Almost Souslin Chromatic number 05A17 Hedetniemi's conjecture Square-Brackets Partition Relations Forcing Rado's conjecture Universal Sequences Dushnik-Miller middle diamond 05D10 Reduced Power Martin's Axiom Erdos Cardinal projective Boolean algebra square Weakly compact cardinal Kurepa Hypothesis Parameterized proxy principle S-Space Foundations Slim tree HOD Rock n' Roll Uniformization Ascent Path PFA(S)[S] polarized partition relation free Boolean algebra Mandelbrot set Singular cardinals combinatorics Almost countably chromatic Small forcing Prikry-type forcing Cardinal function b-scale Fast club Coherent tree Diamond Antichain Rainbow sets Luzin set 11P99 Knaster Postprocessing function Souslin Tree Partition Relations Aronszajn tree Microscopic Approach Cohen real L-space weak diamond Club Guessing stationary reflection reflection principles incompactness xbox Selective Ultrafilter coloring number P-Ideal Dichotomy Constructible Universe Non-saturation Distributive tree Fat stationary set approachability ideal Jonsson cardinal Axiom R sap very good scale Whitehead Problem OCA Erdos-Hajnal graphs Stevo Todorcevic Poset Large Cardinals Forcing Axioms Nonspecial tree stationary hitting Singular coﬁnality Fodor-type reflection Hereditarily Lindelöf space tensor product graph

# 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