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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

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

# 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