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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

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

# 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