1 citations · 1 across the 12 of their papers we have counts for
18 papers
Fixed Sets of Automorphisms of Countable, Arithmetically Saturated Structures
James Schmerl
We characterize the fixed sets of automorphisms of an arbitrary countable, arithmetically saturated structure.
Fixed Sets of Automorphisms of Countable, Arithmetically Saturated Structures
James H. Schmerl
If an automorphism f of a structure M is such that fix(f^k) = fix(f) for all positive k, then M|fix(f) is a substructure of M. The possible isomorphism types of such M|fix(f) are c…
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 $\mat…
The Pentagon as a Substructure Lattice of Models of Peano Arithmetic
James H. Schmerl
Wilke proved in 1977 that every countable model of Peano Arithmetic has an elementary end extension such that the interstructure lattice Lt(${\mathcal…
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 $…
A Remark on a Theorem of Erdos
James H. Schmerl
A theorem of Erdos asserts that every infinite subset of Euclidean n-space R^n has a subset of the same cardinality having no repeated distances. This theorem is generalized here a…
Cofinal Extensions and Coded Sets
James H. Schmerl
Let M be a model of Peano Arithmetic that is countably generated over an exponentially closed cut I. We characterize those sets X of subsets of I for which there is a finitely (or…
Deciding the Chromatic Numbers of Algebraic Hypergrahs
James H. Schmerl
For each infinite cardinal k, the set of algebraic hypergraphs having chromatic number no larger than k is decidable.
Minimal elementary end extensions
James H. Schmerl
Suppose that is a model of PA and is a countably generated elementary end extension of . Let be the set of subsets of M…
Self-embeddings of computable trees
Stephen Binns, Bjørn Kjos-Hanssen, Manuel Lerman +2
We divide the class of infinite computable trees into three types. For the first and second types, computes a nontrivial self-embedding while for the third type computes…
Chromatic Numbers of Algebraic Hypergraphs
James H. Schmerl
A k-uniform hypergraph is algebraic if its vertex set is n-dimensional Euclidean space, for some n, and its hyperedge set is defined from the zero set of some polynomial. The chrom…
Semialgebraic Graphs having Countable List-Chromatic Numbers
James H. Schmerl
The set of semialgebraic graphs having countable list-chromatic numbers is characterized. Some other related sets of graphs having countable list-chromatic numbers also are.
Uncountable Real Closed Fields with PA Integer Parts
David Marker, James Schmerl, Charles Steinhorn
D'Aquino, Knight and Starchenko classified the countable real closed fields with integer parts that are nonstandard models of Peano Arithmetic. We rule out some possibilities for e…
The Automorphism Group of a Resplendent Model
James H. Schmerl
The first-order theory of the automorphism group of an infinite resplendent model in a finite language is undecidable.