In this conference report a summary is given on the theoretical work that has contributed to provide accurate theoretical predictions for testing the standard model in present and future experiments. Precision calculations for the vector boson masses, for the Z resonance, W pair production, and for the g − 2 of the muon are reviewed and the theoretical situation for the Higgs sector is summariz...

The model theory of abelian groups was developed by Szmielew ([28] quantifier elimination and decidability) and Eklof & Fisher [4], who observed that K1saturated abelian groups are pure injective. Eklof & Fisher related the structure theory of pure injective abelian groups with their model theory. The extension of this theory to modules over arbitrary rings became possible after the work of Bau...

This article introduces some of the basic concepts and results from model theory, starting from scratch. The topics covered are be tailored to the model theory of fields and later articles. I will be using algebraically closed fields to illustrate most of these ideas. The tools described are quite basic; most of the material is due either to Alfred Tarski or Abraham Robinson. At the end I give ...

In general, a product has a different theory to that of the structures in the set Mi. For example a product of fields is just a ring. Note also that if φ is an atomic formula then ∏ iMi |= φ((ai )i, · · · , (ai )i) iff {i ∈ I : Mi |= φ(ai , · · · , ai )} = I. In particular this shows that if J ⊆ I then the restiction function (ai)i∈I → (ai)i∈J is a surjective homomorphism from ∏ i∈IMi to ∏ i∈JM...

This paper summarizes the theoretical background that is used in several applications listed in the sibling conference paper [1]. We investigate object simplification methods based on Centroidal Voronoi Tesselation (CVT) that share the possibility of great speed-ups in various scenarios. We propose Constrained CVT to sample points from the object boundary and the Region-based CVT to be able to ...

In this paper, we study metric structures with a nite number of metrics by extending the model theory developed by Ben Yaacov et al. in the monograph Model theory for metric structures. We rst de ne a metric structure with nitely many metrics, develop the theory of ultraproducts of multimetric structures, and prove some classical model-theoretic theorems about saturation for structures with mul...

We consider the restriction of first–order logic to models, called pseudo– finite, with the property that every first–order sentence true in the model is true in a finite model. We argue that this is a good framework for studying first-order logic on finite structures. We prove a Lindström Theorem for extensions of first order logic on pseudo-finite structures.

Course Description: An important branch of mathematical logic is model theory, the study of first-order theories and the classes of models defined by such theories. This course will include numerous applications of model theory to algebra, especially ordered fields and differential fields. All of the necessary background in mathematical logic and algebra will be presented in detail. Among the h...

These notes aim at giving the basic definitions and results from model theory. My intention in writing them, is that they should provide the reader with many examples, even with some proofs, and contain most of the definitions. Differences in vocabulary can be quite an obstacle to mutual understanding, and having the terminology written up somewhere should prove helpful. An index is included at...

In this paper we emphasize the links between model theory and tilings. More precisely, after giving the definitions of what tilings are, we give a natural way to have an interpretation of the tiling rules in first order logics. This opens the way to map some model theoretical properties onto some properties of sets of tilings, or tilings themselves.