nLab constructible set

Contents

Idea

Constructible sets are one of the central notions in descriptive set theory.

In set theory, a (Gödel) constructible set is any set in a constructible universe, see there.

One can generalize to constructible elements in more general Boolean lattices.

In general topology, given a topological space $(X,\tau)$ , a constructible subset of $X$ , sometimes (when $(X,\tau)$ is fixed) often simply referred as a constructible set, is an element of the smallest Boolean algebra of sets containing the topology $\tau$ ; the constructible sets are precisely the finite unions of locally closed sets.
In the case of theory ACF of algebraically closed fields, for every model $K$ , the constructible sets in the affine space $K^n$ are precisely the definable sets for the language of fields.

Last revised on November 15, 2023 at 09:38:42. See the history of this page for a list of all contributions to it.