# Tagged Questions

33 views

### Some small (and probably easy) implication from combinatorics paper

I'm reading https://people.math.osu.edu/bergelson.1/PolSz.pdf . Question is about part from (1.7) on page 16. Why $\lambda(\chi_{1})=\lambda(\chi_{1})$? There's no problem if in 4-th verse ...
88 views

### Reconciling two statements of Ramsey's Theorem.

In the appendix to Shelah's book on Classification Theory: THEOREM 2.1 (Ramsey's Theorem): (1) For any infinite ordered set $I$, and $n$-place function $f$ from $I$, with range of cardinality ...
792 views

### Why König's lemma isn't “obvious”?

I keep facing König's lemma "Every finitely branching infinite tree over $\mathbb{N}$ has infinite branch". Why it is not taken "obvious" but needs a careful proof? It seems somewhat obvious, but I ...
For $k=2$, from this post A "geometrical" representation for Ramsey's theorem, how one can deduce the theorem from Constant $f:[\mathbb{N}]^2\to \{1,2\}$ (part 2), or by knowing that ...
Suppose $f:\mathbb{Z}^+\longrightarrow X$ is a function, with $X$ a finite set. Is it true that there are $a,b\in\mathbb{Z}^+$ such that $f(a)=f(b)=f(a+b)$.