3 papers
math.LO2014
Positive model theory and infinitary logic
Jean Berthet
We study the basic properties of a dual "spectral" topology on positive type spaces of h-inductive theories and its essential connection to infinitary logic. The topology is Hausdo…
math.RA2013
Geometrically closed rings
Jean Berthet
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…
math.LO2012
Prime types and geometric completeness
Jean Berthet
The geometric form of Hilbert's Nullstellensatz may be understood as a property of "geometric saturation" in algebraically closed fields. We conceptualise this property in the lang…