Brendan Cordy

Department of Mathematics
Marianopolis College
4873 Westmount Ave
Westmount, QC, H3Y 1X9



Tarski's Theorem

Tarski's theorem on the undefinability of truth in arithmetic is a result that has, in popular mathematics literature, been almost completely eclipsed by the first incompleteness theorem. This is unfortunate, because a complete exposition of the first incompleteness theorem requires so much more overhead. Tarski's theorem is no less profound and includes all of the cute coding tricks, as well as the same diagonal argument used in the proof the the first incompleteness theorem; however, assuming some experience with first-order logic, it only takes a few pages to get to the proof of Tarski's theorem.

If you're interested in reading about it, you can find my exposition of Tarski's theorem here.

Interactive z-Table

This is a visual version of the z-table, written in javascript. Click the red dots on the horizontal axis to pick your favourite interval. In its current form, it runs very slowly in firefox for some reason.

Category Theory Notes

A few years ago I ran an informal summer course introducing graduate students in computer science to category theory. I made a set of notes complete with exercises, and now they're just sitting in a desk. I started TeXing these, but that project is currently on hold. The Barr & Wells book Category Theory for Computing Science is now freely available, and I highly recommend it.

If you happen to be seeking some online category theory literature, you might want to take a look at this section of Alexander Kurz's webpage.

Thesis

My master's thesis is concerned with coalgebraic modal logic. The idea is to realize a certain class of structures as the class of coalgebras for an endofunctor, and from that functor extract an adequate and expressive modal logic for reasoning about said structures, along with a complete system of inference. In my thesis I do this explicitly for deterministic Kripe machines. The ultimate goal is to find a uniform way of doing this for as many classes of structures as possible. A few of the most influential people involved in this program are Jan Rutten, Alexander Kurz, and Dirk Pattinson.

Older Papers

On the existence of regular approximations is a paper I co-authored with Kai Salomaa and presented at DCFS 2006. In the paper we introduce an asymptotic measure of how close a given formal language is to being a regular language, and explore properties of this measure.