example of definable type
The theory of has quantifier elimination, and so is o-minimal. Thus a type over the set is determined by the quantifier free formulas over , which in turn are determined by the atomic formulas over . An atomic formula in one variable over is of the form or or for some . Thus each 1-type over determines a Dedekind cut over , and conversely a Dedekind cut determines a complete type over . Let .
Thus there are two classes of type over .
Ones where is of the form or for some . It is clear that these are definable from the above discussion.
Ones where has no supremum in . These are clearly not definable by o-minimality of .
|Title||example of definable type|
|Date of creation||2013-03-22 13:29:43|
|Last modified on||2013-03-22 13:29:43|
|Last modified by||aplant (12431)|