Graduate studies at Western
Journal of Symbolic Logic 52 (2):512-518 (1987)
|Abstract||This paper continues the investigation of inconsistent arithmetical structures. In $\S2$ the basic notion of a model with identity is defined, and results needed from elsewhere are cited. In $\S3$ several nonisomorphic inconsistent models with identity which extend the (=, $\S4$ inconsistent nonstandard models of the classical theory of finite rings and fields modulo m, i.e. Z m , are briefly considered. In $\S5$ two models modulo an infinite nonstandard number are considered. In the first, it is shown how to model inconsistently the arithmetic of the rationals with all names included, a strengthening of earlier results. In the second, all inconsistency is confined to the nonstandard integers, and the effects on Fermat's Last Theorem are considered. It is concluded that the prospects for a good inconsistent theory of fields may be limited|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
V. Kanovei (1995). Uniqueness, Collection, and External Collapse of Cardinals in Ist and Models of Peano Arithmetic. Journal of Symbolic Logic 60 (1):318-324.
Vladimir Kanovei (1996). On External Scott Algebras in Nonstandard Models of Peano Arithmetic. Journal of Symbolic Logic 61 (2):586-607.
H. Jerome Keisler (2006). Nonstandard Arithmetic and Reverse Mathematics. Bulletin of Symbolic Logic 12 (1):100-125.
Stuart T. Smith (1987). Nonstandard Characterizations of Recursive Saturation and Resplendency. Journal of Symbolic Logic 52 (3):842-863.
Andreas Blass (1974). On Certain Types and Models for Arithmetic. Journal of Symbolic Logic 39 (1):151-162.
Graham Priest (2000). Inconsistent Models of Arithmetic. Part II: The General Case. Journal of Symbolic Logic 65 (4):1519-1529.
Shizuo Kamo (1981). Nonstandard Natural Number Systems and Nonstandard Models. Journal of Symbolic Logic 46 (2):365-376.
C. Ward Henson, Matt Kaufmann & H. Jerome Keisler (1984). The Strength of Nonstandard Methods in Arithmetic. Journal of Symbolic Logic 49 (4):1039-1058.
Jeremy Avigad & Jeffrey Helzner (2002). Transfer Principles in Nonstandard Intuitionistic Arithmetic. Archive for Mathematical Logic 41 (6):581-602.
Added to index2009-01-28
Total downloads6 ( #154,770 of 722,942 )
Recent downloads (6 months)1 ( #61,087 of 722,942 )
How can I increase my downloads?