#
Definability and decidability problems in number theory

May 6 to May 10, 2019
at the

American Institute of Mathematics,
San Jose, California

organized by

Kirsten Eisentraeger,
Valentina Harizanov,
Jennifer Park,
and Alexandra Shlapentokh

## Original Announcement

This workshop will be devoted to definability and decidability problems in number theory.
The main topics for the workshop are

- H10 and existential definability of $\mathbb{Z}$ for $\mathbb{Q}$ and big subrings of $\mathbb{Q}$.
- Decidability of the first-order and the existential theory in finite and infinite algebraic extensions of $\mathbb{Q}$.
The workshop will bring together mathematicians working in algebraic geometry, number theory, model theory and computability theory to work on problems in decidability/computability and definability in number theory.
- Definability of valuation rings over infinite algebraic extensions of $\mathbb{Q}$ and over function fields.

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.

A list of open problems.