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### 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

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

# 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