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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

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

# 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