Filling certain cuts in discrete weakly o-minimal structures

摘要

Discrete weakly o-minimal structures, although not so stimulating as their dense counterparts, do exhibit a certain wealth of examples and pathologies. For instance they lack prime models and monotonicity for definable functions, and are not preserved by elementary equivalence. First we exhibit these features. Then we consider a countable theory of weakly o-minimal structures with infinite definable discrete (convex) subsets and we study the Boolean algebra of definable sets of its countable models.