# My Notes

Here are some notes I've written. They were written mostly for myself, so they will have varying levels of readability.

Here are some notes I've written. They were written mostly for myself, so they will have varying levels of readability.

Morley Rank as a Game - A cat and a mouse play a game to figure out how slippery a type over a complete theory T is. The notion of Morley rank is recovered from this.

On Small Models of Theories - An exploration on what it means of a model of a theory to be "small", yielding a very ad-hoc definition which turns out to be equivalent to atomic in the case of countable languages.

The Characterization of Computation via Predicates And Some Consequences - Some notes on GĂ¶del's first incompleteness theorem and Tennenbaum's theorem on the nonexistence of nonstandard models of PA. Some parts are blatantly unfinished, but I think it's solid work.

A Proof of the Low Basis Theorem and Another Proof of the Low Basis Theorem - I was having a hard time understanding this theorem, so I wrote two proofs of it in different styles. I still can't quite say I entirely get it, but at least I'm convinced that a proof exists!

A Quick Writeup on Ordinals - A proof that every order-type of a well-ordered set has a canonical representative.

Encoding Finite Sequences in RCA0 - Title.

A Proof that Solutions to Smooth ODEs are Smooth - Title.

Solutions to a couple of tricky exercises from Odifreddi's book (Classical Recursion Theory) - III.2.19(a), III.3.9(c).

A minimal degree below 0' - Where I take 8 pages to do what Soare does in one.

Any Low k-quasidiscrete Order is Computable - There was this proof in a paper that I had a hard time understanding, so I wrote it down.

E-mail: dmaia@uchicago.edu