Topic Archive: interstices
We define the notion of a regular interstice and show that every regular interstice has elements realizing selective types.
I will present a generalization of the notion of interstices that
originated from the study of generic cuts.
Let M be a model of PA for which Th(M) is not Th(N) (N is the standard model). Then M has nonstandard definable elements. Let c be a non-definable element. The largest convex set which contains c and no definable elements is called the interstice around c. In this talk we discuss various properties of interstices. We also define intersticial gaps which are special subsets of interstices. We show that the set of the intersticial gaps which are contained in any given interstice of a countable arithmetically saturated model of PA is a dense linear order.