## Journal of Symbolic Logic

### Quantifier Elimination in Tame Infinite p-Adic Fields

Ingo Brigandt

#### Abstract

We give an answer to the question as to whether quantifier elimination is possible in some infinite algebraic extensions of $\mathbb{Q}_p$ ('infinite p-adic fields') using a natural language extension. The present paper deals with those infinite p-adic fields which admit only tamely ramified algebraic extensions (so- called tame fields). In the case of tame fields whose residue fields satisfy Kaplansky's condition of having no extension of p-divisible degree quantifier elimination is possible when the language of valued fields is extended by the power predicates P$_n$, introduced by Macintyre and, for the residue field, further predicates and constants. For tame infinite p-adic fields with algebraically closed residue fields an extension by P$_n$ predicates is sufficient.

#### Article information

Source
J. Symbolic Logic, Volume 66, Issue 3 (2001), 1493-1503.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183746574

Mathematical Reviews number (MathSciNet)
MR1856756

Zentralblatt MATH identifier
0993.03050

JSTOR