Mathematical Logic Quarterly 51 (2):145 (2005)

Abstract
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 subsets and we study the Boolean algebra of definable sets of its countable models
Keywords weakly o‐minimal theory  Discrete order  p‐ω‐categorical theory  Boolean algebra
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DOI 10.1002/malq.200410014
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