Indice degli argomenti
Program/abstract
Let L be a first-order 2-sorted language. Let X be some fixed structure.A standard structure is an L-structure of the form ⟨M,X⟩.
When X is a compact topological space (and L meets a few additional requirements) it is possible to adapt a significant part of model theory to the class of standard structures. In the last 20 years the most popular approach uses real-valued logic (Ben Yaacov, Berenstein, Henson, Usvyatsov).
In this course we present a different, more general, approach which only uses classical logic. This is based on three facts:
Every standard structure has a positive elementary extension that is standard and realizes all positive types that are finitely consistent.
In a sufficiently saturated structure, the negation of a positive formula is equivalent to an infinite disjunction of positive formulas.
There is a pure model theoretic notion that corresponds to Cauchy completeness.
To exemplify how this setting applies to model theory we discuss ω-categoricity and (local) stability. We will revisit the classical theory and compare it with the continuous case.
Lezione 15 novembre ore 15:00
Lezione 29 novembre ore 15:00
Lezione 6 dicembre ore 15:00
Argomento 4
Argomento 5