Models of : when two elements are necessarily order automorphic
Saharon Shelah · Mathematical logic quarterly · 2015
We are interested in the question of how much the order of a non‐standard model of can determine the model. In particular, for a model M, we want to characterize the complete types of non‐standard elements such that the linear orders and are necessarily isomorphic. It is proved that this set includes the complete types such that if the pair realizes it (in M) then there is an element c such that for all standard n, , , , and . We prove that this is optimal, because if holds, then there is M of cardinality ℵ1 for which we get equality. We also deal with how much the order in a model of may determine the addition.