Pseudo real closed fields, pseudo p-adically closed fields and NTP2

Cross-Sections for p-Adically Closed Fields

and cross-section g g G ¬ t. w x If p is prime, a p-valued field 8, p. 7 is a valued field, of characteristic zero, in which p has minimal positive value and whose residue field has p Ž . elements. A p-valued field F, ̈ is p-adically closed just in case no algebraic extension F9 of F with valuation ̈ 9 extending ̈ is p-valued. The Ž . class of p-adically closed fields is to Q , ̈ as the class of re...

HENSELIAN RESIDUALLY p-ADICALLY CLOSED FIELDS

In (Arch. Math. 57 (1991), pp. 446–455), R. Farré proved a positivstellensatz for real-series closed fields. Here we consider p-valued fields 〈K, vp〉 with a non-trivial valuation v which satisfies a compatibility condition between vp and v. We use this notion to establish the p-adic analogue of real-series closed fields; these fields are called henselian residually p-adically closed fields. Fir...

The Elementary Theory of Free Pseudo p-adically Closed Fields of Finite Corank

Pseudo Algebraically Closed Fields over Rings

We prove that for almost all σ ∈ G(Q)e the field Q̃(σ) has the following property: For each absolutely irreducible affine variety V of dimension r and each dominating separable rational map φ: V → Ar there exists a point a ∈ V (Q̃(σ)) such that φ(a) ∈ Zr. We then say that Q̃(σ) is PAC over Z. This is a stronger property then being PAC. Indeed we show that beside the fields Q̃(σ) other fields which ...

PSEUDO ALGEBRAICALLY CLOSED FIELDS OVER RINGSbyMoshe

We prove that for almost all 2 G(Q) e the eld ~ Q() has the following property: For each absolutely irreducible aane variety V of dimension r and each dominating separable rational map ': V ! A r there exists a point a 2 V (~ Q()) such that '(a) 2 Z r. We then say that ~ Q() is PAC over Z. This is a stronger property then being PAC. Indeed we show that beside the elds ~ Q() other elds which are...