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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

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

# 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