Arno Fehm (TAU)
Towards decidability of fields of totally S-adic numbers

Abstract:
First we survey previous decidability results for theories of fields of
algebraic numbers and the methods employed there. Then we introduce
certain fields of totally S-adic numbers and sketch a plan how to
generalize these methods to show decidability for those fields, using
very recent results on their absolute Galois groups and local-global
principles they satisfy.