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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

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

# 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