# Meeting Details

Title: Unions of chains of signatures Logic Seminar Alice Medvedev, University of California, Berkeley We meditate on a particularly naive notion of a limit of a sequence of theories: a union of conservative expansions. That is, we consider a sequence of nested signatures $L_1 \subset L_2 \subset \ldots$, each one a subsignature of the next, and a sequence of $L_i$-theories $T_i$ where each $T_i$ is precisely the set of $L_i$-consequences of $T_{i+1}$. It turns out that many model-theoretic properties then pass from all $T_i$ to their union $T$; these include consistency, completeness, quantifier limination, partial quantifier elimination such a model-completeness, elimination of imaginaries, stable embeddedness of some definable set, characterization of algebraic closure; stability, simplicity, rosiness, dependence. Our motivating example is the theory $T$ of fields with an action by $(\mathbb{Q}, +)$, seen as a limit of (theories of) fields with $(\mathbb{Z}, +)$-actions.