Archives for July 2010

Infinite trees are $E_3$ (maybe)

Not completely sure about this, but here we go: I will show that an ordered, plane recursive tree is $E_n$-computable, $n \geq 3$, if each vertex has its number of children bounded by an $E_n$ function. So this rules out …

Lists and finite trees are $E_3$

In order to prove the fgoagog thing we need to be able to do computations on trees at a low level of the Grzegorczyk hierarchy, so it doesn’t mess up the complexity of the whole group computation. I will give …

Computable categories

So I read a bit about categories after Peter Hines came up to talk to us.

Categories

A category $C$ is a collection of objects $obj(C)$ (or just Obj), a collection of arrows (or morphisms) $hom(C)$ (or just Hom)