9 papers
The Diversity of Minimal Cofinal Extensions
James H. Schmerl
Fix a countable nonstandard model of Peano Arithmetic. Even with some rather severe restrictions placed on the types of minimal cofinal extensions $\mathcal N \succ \m…
CP-generic expansions of models of Peano Arithmetic
Athar Abdul-Quader, James H. Schmerl
We study notions of genericity in models of , inspired by lines of inquiry initiated by Chatzidakis and Pillay and continued by Dolich, Miller and Steinhorn in general…
Lofty Models of Peano Arithmetic
James H. Schmerl
If M is a nonstandard model of Peano Arithmetic, then M is lofty iff M has a simple elementary extension that is recursively saturated. This had previously been known for countable…
The Barwise-Schlipf Theorem
Ali Enayat, James H. Schmerl
In 1975 Barwise and Schlipf published a landmark paper whose main theorem asserts that a nonstandard model of PA (Peano arithmetic) is recursively saturated iff $\mat…
Kernels, Truth and Satisfaction
James H. Schmerl
The notions of the kernel of a graph, full truth sets and full satisfaction sets are connected.
Acceptable colorings of indexed hyperspaces
James H. Schmerl
Previous results about -grids with acceptable colorings are extended to -indexed hyperspaces, which are structures , where each $…