2,930 research outputs found
Geometrically closed rings
We develop the basic theory of geometrically closed rings as a generalisation
of algebraically closed fields, on the grounds of notions coming from positive
model theory and affine algebraic geometry. For this purpose we consider
several connections between finitely presented rings and ultraproducts, affine
varieties and definable sets, and we introduce the key notion of an arithmetic
theory as a purely algebraic version of coherent logic for rings.Comment: 18 page
Arithmetic-arboreal residue structures induced by Prufer extensions : An axiomatic approach
We present an axiomatic framework for the residue structures induced by
Prufer extensions with a stress upon the intimate connection between their
arithmetic and arboreal theoretic properties. The main result of the paper
provides an adjunction relationship between two naturally defined functors
relating Prufer extensions and superrigid directed commutative regular
quasi-semirings.Comment: 56 page
Games for the Strategic Influence of Expectations
We introduce a new class of games where each player's aim is to randomise her
strategic choices in order to affect the other players' expectations aside from
her own. The way each player intends to exert this influence is expressed
through a Boolean combination of polynomial equalities and inequalities with
rational coefficients. We offer a logical representation of these games as well
as a computational study of the existence of equilibria.Comment: In Proceedings SR 2014, arXiv:1404.041
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