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### 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
- Genearlizations 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

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

# 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