I am a postdoctoral fellow working in algebra and representation theory at the University of Melbourne in Australia. Some of the topics I like include ring theory, module theory, p-adic groups, logic, combinatorics, and most other topics in algebra. I like analysis as well but I don’t get much of an opportunity to do that stuff. I like writing about mathematics, which is why I created this blog.

For access to my papers and more on my academic research, I invite you to visit jpolak.org.

The primary purpose of this blog is to showcase mathematical abstraction and its beauty in the realm of pure mathematics, especially in algebra.

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.

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!