### Archives

### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# Tag Archives: Universal Sequences

## Universal binary sequences

Notation. Write $\mathcal Q(A):=\{ a\subseteq A\mid a\text{ is finite}, a\neq\emptyset\}$. Suppose for the moment that we are given a fixed sequence $\langle f_\alpha:\omega\rightarrow2\mid \alpha\in a\rangle$, indexed by some set $a$ of ordinals. Then, for every function $h:a\rightarrow\omega$ and $i<\omega$, we … Continue reading

## 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