Seminar series
Date
Thu, 19 May 2016
17:30
Location
L6
Speaker
Marcus Tressl
Organisation
Manchester

An abelian l-group G is essentially a partially ordered subgroup of functions from a set to a totally ordered abelian group such

that G is closed under taking finite infima and suprema. For example, G could be the continuous semi-linear functions defined on the open
unit square, or, G could be the continuous semi-algebraic functions defined in the plane with values in (0,\infty), where the group
operation is multiplication. I will show how G, under natural geometric assumptions, can be interpreted (in a weak sense) in its lattice of
zero sets. This will then be applied to the model theory of natural divisible abelian l-groups. For example we will see that the
aforementioned examples are elementary equivalent. (Parts of the results have been announced in a preliminary report from 1987 by F. Shen
and V. Weispfenning.)

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