1. Lattice Ordered O-Minimal Structures
- Author
-
Carlo Toffalori
- Subjects
Join and meet ,Combinatorics ,Crystallography ,Logic ,Incidence algebra ,Lattice (order) ,Boolean algebras canonically defined ,Complete Boolean algebra ,Total order ,Map of lattices ,03C64 ,Mathematics ,Complemented lattice - Abstract
We propose a notion of $o$-minimality for partially ordered structures. Then we study $o$-minimal partially ordered structures $(A, \leq, \ldots)$ such that $(A,\leq)$ is a Boolean algebra. We prove that they admit prime models over arbitrary subsets and we characterize $\omega$-categoricity in their setting. Finally, we classify $o$-minimal Boolean algebras as well as $o$-minimal measure spaces.
- Published
- 1998