We study the stability of a sequence of integral functionals on divergence-free matrix valued fields following the direct methods of Γ-convergence. We prove that the Γ-limit is an integral functional on divergence-free matrix valued fields. Moreover, we show that the Γlimit is also stable under volume constraint and various type of boundary conditions.

We investigate the embeddings of the value group and residue field of a real closed valued field A in Aeq via quantifier elimination in a three sorted language. We classify the one types of field elements in a real closed valued field. Finally, we investigate some of the linear structure in Aeq induced by the valuation ring V and introduce the geometric sorts. In a subsequent paper we show that...

These notes are intended to accompany the tutorial series ‘Model theory of algebraically closed valued fields’ in the Workshop ‘An introduction to recent applications of model theory’, Cambridge March 29–April 8, 2005. They do not contain any new results, except for a slightly new method of exposition, due to Lippel, of parts of the proof of elimination of imaginaries, in Sections 8 and 9. They...

A central feature of current object-oriented languages is the ability to dynamically instantiate user-defined container data structures such as lists, trees, and hash tables. Implementations of these data structures typically use references to dynamically allocated objects, which complicates reasoning about the resulting program. Reasoning is simplified if data structure operations are specifie...

Let F be a field complete for a real valuation. It is a standard result in valuation theory that a finite extension of F admits a valuation basis if and only if it is without defect. We show that even otherwise, one can construct bases in which the discrepancy between measuring valuation an element versus on the components in its basis decomposition can be made arbitrarily small. The key step i...

An important feature of object-oriented programming languages is the ability to dynamically instantiate user-defined container data structures such as lists, trees, and hash tables. Programs implement such data structures using references to dynamically allocated objects, which allows data structures to store unbounded numbers of objects, but makes reasoning about programs more difficult. Reaso...

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A henselian valued field K is called separably tame if its separable-algebraic closure K is a tame extension, that is, the ramification field of the normal extension K|K is separable-algebraically closed. Every separable-algebraically maximal Kaplansky field is a separably tame field, but not conversely. In this paper, we prove Ax– Kochen–Ershov Principles for separably tame fields. This leads ...