MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I apologize if this is not the right forum to ask such a basic question... In model theory what does that mean that a type concentrates on one point?

share|cite|improve this question
It probably means that there exists a single formula which axiomatizes the type (i.e., the type consists of the consequences of the formula), though I can’t recall seeing this particular terminology for this concept known under lots of other various names (e.g., isolated type, principal type). – Emil Jeřábek May 23 '11 at 17:52
Although, if the type is not assumed to be complete, it may (or may not) be that the term only means that the type is included in a principal type, and OTOH, it may (or may not) be that the generating formula is required to be complete. More context would really help. – Emil Jeřábek May 23 '11 at 18:05
Thank you for your ansswers. The type is supposed to be definable. I'm sorry I should have mentionned it maybe the notion of limit of a type makes sense otherwise. I've found this definition: M is an o-minimal structure. A point a of $M^n$ is a limit of p a definable type if for any definable neighborhood U of a (defined with parameters), p concentrates on U. The context is the following theorem: let M be an o-minimal structure, $ X \subset M^n$ then the fact that X is closed and bounded, is equivalent to the fact that any definable type concentrates on one point. – over May 30 '11 at 2:10
I know that this is equivalent to a third fact that is: any M-definable curve in X is completable. ($ X \subset M^n$ with M be an o-minimal structure) (a curve in X is a M-definable continuous embedding f: $(a,b) \stackrel{}{\rightarrow} X$ where (a,b)$\subset$M. It is said to be completable if $\lim_{x\rightarrow a^{+}} f (x) $ and $\lim_{x\rightarrow b^{-}} f (x)$ exist.) I've been told one can associate a definable type to such a curve. But I'm not sure of how. %aybe this would help to understand it? – over May 30 '11 at 2:11

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.