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Point, Françoise
Published in
Archive for Mathematical Logic

Given a model-complete theory of topological fields, we considered its generic differential expansions and under a certain hypothesis of largeness, we axiomatised the class of existentially closed ones. Here we show that a density result for definable types over definably closed subsets in such differential topological fields. Then we show two tran...

Macpherson, Dugald
Published in
Archive for Mathematical Logic

This is a survey, intended both for group theorists and model theorists, concerning the structure of pseudofinite groups, that is, infinite models of the first-order theory of finite groups. The focus is on concepts from stability theory and generalisations in the context of pseudofinite groups, and on the information this might provide for finite ...

Thuong, Lê Quy
Published in
Acta Mathematica Vietnamica

In Kontsevich-Soibelman’s theory of motivic Donaldson-Thomas invariants for 3-dimensional noncommutative Calabi-Yau varieties, the integral identity conjecture plays a crucial role as it involves the existence of these invariants. A purpose of this note is to show how the conjecture arises. Because of the integral identity’s nature, we shall give a...

Quackenbush, Robert W.
Published in
Algebra universalis

Algebraically closed abelian groups are precisely the divisible abelian groups; the underlying groups of rational vector spaces are precisely the divisible abelian groups. That is, rational vector spaces are the skolemization of algebraically closed abelian groups, obtained by adding scalar multiplication by each rational to the set of operations. ...

Yin, Yimu
Published in
Selecta Mathematica

We continue the study of the Hrushovski–Kazhdan integration theory and consider exponential integrals. The Grothendieck ring is enlarged via a tautological additive character and hence can receive such integrals. We then define the Fourier transform in our integration theory and establish some fundamental properties of it. Thereafter, a basic theor...