Discrete Weakly O-Minimal Structures

The talk focuses on the general behavior of discrete weakly o-minimal structures, and their definable sets and functions. Comparisons are drawn with the dense weakly o-minimal case and with the discrete o-minimal case. We develop tools to describe definable maps in these structures, and ultimately state a prove a monotonicity theorem. We also state, using the results given so far, how we hope to prove that no definable groups exist in the discrete, weakly o-minimal setting.