Externally definable quotients and NIP expansions of the real ordered additive group

On Continuous Functions Definable in Expansions of the Ordered Real Additive Group

Let R be an expansion of the ordered real additive group. Then one of the following holds: either every continuous function [0, 1] → R definable in R is C2 on an open dense subset of [0, 1], or every C2 function [0, 1] → R definable in R is affine, or every continuous function [0, 1] → R is definable in R. If R is NTP2 or more generally does not interpret a model of the monadic second order the...

Expansions of the Ordered additive Group of Real numbers by two discrete Subgroups

The theory of (R, <,+,Z,Za) is decidable if a is quadratic. If a is the golden ratio, (R, <,+,Z,Za) defines multiplication by a. The results are established by using the Ostrowski numeration system based on the continued fraction expansion of a to define the above structures in monadic second order logic of one successor. The converse that (R, <,+,Z,Za) defines monadic second order logic of one...

Definable and Invariant Types in Enrichments of NIP Theories

Definable Additive Categories

This is essentially the talk I gave on definable additive categories; I define these categories, say where they came from, describe some of what is around them and then point out the 2-category which

Ordered Quotients and the Semilattice of Ordered Compactifications

Douglas D. MOONEY, Thomas A. RICHMOND Western Kentucky University Bowling Green, KY 42101 USA The ideas of quotient maps, quotient spaces, and upper semicontinuous decompositions are extended to the setting of ordered topological spaces. These tools are used to investigate the semilattice of ordered compactifications and to construct ordered compactifications with o-totally disconnected and o-z...