About

About the blog

I started Aleph Zero Categorical in 2011 when I was started my PhD in mathematics at McGill University. The primary purpose of this blog is to showcase mathematical abstraction and its beauty in the realm of pure mathematics, especially in algebra. Most of this blog is written to be comprehensible by someone who has taken algebra in graduate school, and much of it can be read with even fewer prerequisites.

Seven years later this blog has not changed much. It is basically an outlet for explaining what I like to think about and read. This blog still exists because I've found I really enjoy writing exposition.

Aleph Zero Categorical, written in symbols as $\aleph_0$ categorical, refers to a concept in model theory called categoricity. For a cardinal $\kappa$, a theory of first order logic is called $\kappa$-categorical if it has only one model of cardinality $\kappa$ up to isomorphism.

A theory with only infinite models that is $\aleph_0$ categorical is complete. This is known as the Vaught-Tarski test.

The tagline "There Can Be Only One" refers to the movie and later television show "Highlander", which was was a frequent phrase uttered throughout the series, and which also was part of the introductory blurb in every episode. This plays on "Aleph Zero Categorical" in that there can be only one countable aleph zero categorical model up to isomorphism.

About the author

I am a Canadian mathematician interested in ring theory, module theory, p-adic groups, logic, combinatorics, and most other topics in algebra. I got my undergraduate degree at the University of Ottawa, and then later my M.Sc. and Ph.D. in mathematics at McGill University.

Some of my other interests include ballroom dancing, birdwatching, photography, piano, and programming.

5 Comments

1. Nguyen Huy Hoang

I'm a graduate student and a math.stackexchange.com member. I know u from ur answer for my question:
http://math.stackexchange.com/questions/514504/example-flat-module-but-neither-projective-nor-injective
I like homological algebra, so can u give me ur Yahoo or Skype to easy commute?
Sorry, my English not good!

2. nice blog, keep up the good work; random suggestion … perhaps make your page header link to some nominated home page (or add a home link) just to ease getting around the site?

• Jason Polak

Thanks for the suggestion. I made the header clickable and added a 'Home' link on the side.

3. "There can be only one" might have made its fair share of appearances on the TV show "Highlander", but its origin lie in the first Highlander movie from 1986 with Christopher Lambert as the titular Highlander, Connor MacLeod.

• Jason Polak

Indeed! However, I believe it's fair to say that when I came up with that tagline, I was thinking of the television show.