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 Gödel'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.