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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
- 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

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

# 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