David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 59 (1):140-150 (1994)
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)
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
M. Krynicki & K. Zdanowski (2005). Theories of Arithmetics in Finite Models. Journal of Symbolic Logic 70 (1):1-28.
Alessandro Berarducci & Margarita Otero (1996). A Recursive Nonstandard Model of Normal Open Induction. Journal of Symbolic Logic 61 (4):1228-1241.
Fred G. Abramson & Leo A. Harrington (1978). Models Without Indiscernibles. Journal of Symbolic Logic 43 (3):572-600.
Erik Ellentuck (1972). An Algebraic Difference Between Isols and Cosimple Isols. Journal of Symbolic Logic 37 (3):557-561.
Erik Ellentuck (1983). Incompatible Extensions of Combinatorial Functions. Journal of Symbolic Logic 48 (3):752-755.
Andreas Blass (1974). On Certain Types and Models for Arithmetic. Journal of Symbolic Logic 39 (1):151-162.
Rod Downey (1989). On Hyper-Torre Isols. Journal of Symbolic Logic 54 (4):1160-1166.
Erik Ellentuck (1974). A Δ02 Theory of Regressive Isols. Journal of Symbolic Logic 39 (3):459 - 468.
Kenneth McAloon (1982). On the Complexity of Models of Arithmetic. Journal of Symbolic Logic 47 (2):403-415.
Erik Ellentuck (1981). Hyper-Torre Isols. Journal of Symbolic Logic 46 (1):1-5.
Added to index2009-01-28
Total downloads4 ( #237,322 of 1,096,452 )
Recent downloads (6 months)3 ( #87,121 of 1,096,452 )
How can I increase my downloads?