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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
- Genearlizations 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

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

# 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