Aleph Zero Categorical is a mathematics blog that I started in 2011. 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 writtent to be comprehensible by someone who has taken algebra in graduate school, and much of it can be read with even fewer prerequisites.

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 old 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. Note that you can't see the tagline in the current theme because I haven't figured out how to make it look cool.

I am a mathematician interested in ring theory, module theory, p-adic groups, logic, combinatorics, and most other topics in algebra. For access to my papers and more on my academic research, I invite you to visit jpolak.org.

I like writing about mathematics, which is why I created this blog. The posts are expository and usually at the undergraduate level. Sometimes I also review math and science books.

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

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!