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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

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

# 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