Abstract
We define certain properties of subsets of models of arithmetic related to their codability in end extensions and elementary end extensions. We characterize these properties using some more familiar notions concerning cuts in models of arithmetic.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
[C] Clote, P.: Partition relations in arithmetic. In: DiPrisco, C.A. (ed.) Proc. 6th Latin American Symposium Caracas, Venezuela. (Lect. Notes Math., vol. 1130, pp. 32–68) Berlin Heidelberg New York: Springer 1985
[KMM] Kirby, L., MacAloon, K., Murawski, R.: Indicators, recursive saturation and expandability. Fund. Math.114, 127–139 (1981)
[KP] Kirby, L., Paris, J.: Initial segments of models of Peano's axioms. In: Lachlan, A., et al. (eds.) Set theory and hierarchy theory. V. (Lect. Notes Math., vol. 619 pp. 211–226) Berlin Heidelberg New York: Springer 1977
[K] Kossak, R.: On extensions of models of strong fragments of arithmetic. Proc. Am. Math. Soc.108, 223–232 (1990)
[P] Paris, J.: Some conservation results for fragments of arithmetic. In: Berline, C., McAloon, K., Ressayre, J.-P. (eds.) Model theory and arithmetic. (Lect Notes Math., vol. 890, pp. 251–262), Berlin Heidelberg New York: Springer 1981
[PK] Paris, J., Kirby L.:∑ n -collection schemas in arithmetic. In: Macintyre, A., Pacholski, L., Paris, J. (eds.) Logic Colloquium '77, North-Holland: Wroclaw, Poland, pp. 199–209
[WP] Wilkie, A., Paris, J.: On the existence of end-extensions of models of bounded induction. In: Fenstad, J., Frolov, I., Hilpinen, R. (eds.) Proceedings of the International Congress of Logic Methodology and Philosophy of Science, Moscow 1987
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kossak, R., Paris, J.B. Subsets of models of arithmetic. Arch Math Logic 32, 65–73 (1992). https://doi.org/10.1007/BF01270396
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01270396