The number of solutions of a given algebro-geometric configuration, when it is finite, does not change upon a small perturbation of the parameters; this persists
even upon specializations that change the topology. The precise formulation of this principle of Poncelet and Schubert required, i.a., the notions of algebraically closed fields, flatness, completenesss, multiplicity. I will explain a model-theoretic version, presented in quite different terms. It applies notably to difference equations involving the Galois-Frobenius automorphism $x^p$, uniformly in a prime $p$. In fixed positive characteristic, interesting technical problems arise that I will discuss if time permits.
- Logic Seminar