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.

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?

  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.

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

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