You are not currently logged in.
Access JSTOR through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Torre Models in the Isols
The Journal of Symbolic Logic
Vol. 59, No. 1 (Mar., 1994), pp. 140-150
Published by: Association for Symbolic Logic
Stable URL: http://www.jstor.org/stable/2275256
Page Count: 11
You can always find the topics here!Topics: Isols, Recursive functions, Increasing functions, Mathematical functions, Recursively enumerable sets, Infinite series, Arithmetic, Peano axioms, Mathematical modeling
Were these topics helpful?See somethings inaccurate? Let us know!
Select the topics that are inaccurate.
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
In  J. Hirschfeld established the close connection of models of the true AE sentences of Peano Arithmetic and homomorphic images of the semiring of recursive functions. This fragment of Arithmetic includes most of the familiar results of classical number theory. There are two nice ways that such models appear in the isols. One way was introduced by A. Nerode in  and is referred to in the literature as Nerode Semirings. The other way is called a tame model. It is very similar to a Nerode Semiring and was introduced in . The model theoretic properties of Nerode Semirings and tame models have been widely studied by T. G. McLaughlin (, , and ). In this paper we introduce a new variety of tame model called a torre model. It has as a generator an infinite regressive isol with a nice structural property relative to recursively enumerable sets and their extensions to the isols. What is then obtained is a nonstandard model in the isols of the Π0 2 fragment of Peano Arithmetic with the following property: Let T be a torre model. Let f be any recursive function, and let fΛ be its extension to the isols. If there is an isol A with fΛ(A)∈ T, then there is also an isol B∈ T with fΛ(B) = fΛ(A).
The Journal of Symbolic Logic © 1994 Association for Symbolic Logic