Recent Questions - MathOverflow

I know there are multiple different frameworks for iterating priority arguments as schemes beyond monstrous priority arguments are too complicated to carry out in a classical manner. From what I know the first of its kind was Harrington's workers type framework, and later the iterated trees framework of Lempp and Lerman. Recently Montalbán introduced true stages which I am no...

I asked here the following:

For every positive integer $n$ let $a_n$ be the number of partitions of an $n \times n$ square into regions of orthogonally connected unit squares. This is the sequence

Let me summarize what I think I understand about constructivism:

"Constructive mathematics" is generally understood to mean a variety of theories formulated in intuitionist logic (i.e., not assuming the law of excluded middle, $\neg\neg A\Rightarrow A$ (LEM)) so that, broadly speaking, in order to prove $A \lor B$ one must prove either $A$ or $B$ ("disjunction propert...

For a finite set $P\subset \mathbb R^2$, write

$$ \nu(P)=\#\{\{p,q\}\subset P: |p-q|=1\}, $$

and

$$ u(n)=\max_{|P|=n}\nu(P). $$

Define

$$ \Delta_n = \sup\{\operatorname{diam}(P): |P|=n,\ \nu(P)=u(n)\}. $$

Thus $\Delta_n$ is the largest possible diameter among extremal $n$-point configurations. Extremizers exist, since the unit-distanc...

A set $S$ is said to be a Relational milieu over set $X$, denoted " $S \ Rm \ X$", if and only if, $S$ is a set of subsets of $X$, that fulfills:

Emptyset: $\varnothing \in S $

Singletons: $\forall y \in X: \{y\} \in S$

Relative complements: $\forall y \in S: X \setminus y \in S$