Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Let $S$ be a proconstructible subsemigroup of $M_n(\mathbb{C})$, that is a subsemigroup which is an intersection of constructible sets. Is $S$ an intersection of constructible subsemigroups?

The question arises from the model theory. The proconstructible sets are the type-definable sets and the constructible sets are the definable ones. It is well known that every type-definable subgroup of $M_n(\mathbb{C})$ is in fact definable (since it is $\omega$-stable) and in general in any stable theory a type-definable group is an intersection of definable subgroups.

Clarification: When I say "intersection of constructible sets", I mean countable intersection.

share|improve this question

Your Answer

 
discard

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

Browse other questions tagged or ask your own question.