# Imaginaries, invariant types and pseudo $$p$$-adically closed fields

@article{Montenegro2018ImaginariesIT,
title={Imaginaries, invariant types and pseudo $$p$$-adically closed fields},
author={Samaria Montenegro and Silvain Rideau},
journal={arXiv: Logic},
year={2018}
}
• Published 1 February 2018
• Mathematics
• arXiv: Logic
In this paper, we give a very general criterion for elimination of imaginaries using an abstract independent relation. We also study germs of definable functions at certain well-behaved invariant types. Finally we apply these tools to the elimination of imaginaries in bounded pseudo-p-adically closed fields.
1 Citations
Un principe d'Ax-Kochen-Ershov imaginaire
• Mathematics
• 2021
We study interpretable sets in henselian and σ-henselian valued fields with value group elementarily equivalent to Q or Z. Our first result is an Ax-Kochen-Ershov type principle for weak elimination

## References

SHOWING 1-10 OF 25 REFERENCES
Imaginaries in bounded pseudo real closed fields
The main result of this paper is that if M is a bounded PRC field then Th(M) eliminates imaginaries in the language of rings expanded by constant symbols.
Definable sets in algebraically closed valued fields: elimination of imaginaries
• Mathematics
• 2006
Abstract It is shown that if K is an algebraically closed valued field with valuation ring R, then Th(K) has elimination of imaginaries if sorts are added whose elements are certain cosets in Kn of
Model theory of difference fields
• Mathematics
• 1999
A difference field is a field with a distinguished automorphism σ. This paper studies the model theory of existentially closed difference fields. We introduce a dimension theory on formulas, and in
Embedding problems over large fields
In this paper we study Galois theoretic properties of a large class of fields, a class which includes all fields satisfying a universal local-global principle for the existence of rational points on
ON FORKING AND DEFINABILITY OF TYPES IN SOME DP-MINIMAL THEORIES
• Mathematics, Computer Science
The Journal of Symbolic Logic
• 2014
It is proved that, in a large class of dp-minimal theories including the p-adics, definable types are dense amongst nonforking types.
GENERIC STABILITY AND STABILITY
• Mathematics, Computer Science
The Journal of Symbolic Logic
• 2014
Two results about generically stable types p in arbitrary theories are proved, one on existence of strong germs and the other an equivalence of forking and dividing, assuming generic stability of p (m) for all m.
Pseudo real closed fields, pseudo p-adically closed fields and NTP2
It is proved that, if M is a bounded PRC or PpC field with exactly n orders or p-adic valuations respectively, then T h ( M ) is strong of burden n, which allows us to explicitly compute the burden of types, and to describe forking.
Imaginaries and definable types in algebraically closed valued fields
The text is based on notes from a class entitled {\em Model Theory of Berkovich Spaces}, given at the Hebrew University in the fall term of 2009, and retains the flavor of class notes. It includes an
A Course in Model Theory
• Mathematics
• 2012
Preface 1. The basics 2. Elementary extensions and compactness 3. Quantifier elimination 4. Countable models 5. Aleph-1-categorical theories 6. Morley rank 7. Simple theories 8. Stable theories 9.
Properties of forking in ω-free pseudo-algebraically closed fields
• Z. Chatzidakis
• Computer Science, Mathematics
Journal of Symbolic Logic
• 2002
The study of pseudo-algebraically closed fields (henceforth called PAC) started with the work of J. Ax, who showed that the infinite models of the theory of finite fields are exactly the perfect PAC fields with absolute Galois group isomorphic to , and gave elementary invariants for their first order theory, thereby proving the decidability of the theorists.