#
Definability and decidability problems in number theory

September 9 to September 13, 2013
at the

American Institute of Mathematics,
Palo Alto, California

organized by

Thomas Scanlon,
Alexandra Shlapentokh,
Xavier Vidaux,
and Carlos Videla

## Original Announcement

This workshop will be devoted to studying definability and decidability questions in number theory, more specifically over rational numbers and
their algebraic extensions, as well as over rings of functions of natural interest.
The main topics for the workshop are:

- (Un)Definability of integers over rational numbers and number fields, Hilbert's Tenth Problem, its stronger and weaker versions (e.g. Buchi's Problem) over rational numbers,
number fields and subrings of number fields
- (Un)Decidability of theories of various rings of functions, including rational function fields over complex numbers and function fields of positive characteristic
- Definability and Decidability in infinite extensions of rational numbers

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.

A list of open problems.

Papers arising from the workshop: