MODNET

Research Training Network in Model Theory

Publications > Preprint server > Preprint Number 1253
Preprint Number 1253
1253. Javier de la Nuez González On expansions of non-abelian free groups by cosets of a finite index
subgroup E-mail: Submission date: 10 July 2017 Abstract: Let F be a finitely generated non-abelian free group and Q a finite quotient. Denote by L_Q the language obtained by adding unary predicates P_q, q in Q to the language of groups. Using a slight generalization of some of the techniques involved in Zlil Sela's solution to Tarski's problem on the elementary theory of non-abelian free groups, we provide a few basic results on the validity of first order entences in the L_Q-expansion of F in which every P_q is interpreted as the preimage of q in F. In particular we prove an analogous result to Sela's generalization of Merzlyakov's theorem on ∀∃-sentences and show that the positive theory depends only on Q and neither on the rank of F nor the particular quotient map. Mathematics Subject Classification: 0E05, 20F65, 03Cxx Keywords and phrases: |

Last updated: July 29 2017 05:05 | Please send your corrections to: |