References
Bezboruah, A., Shepherdson, J.C.: Gödel's second incompleteness theorem forQ. J. Symb. Logic41, 503–512 (1976)
Hájek, P.: Positive results on fragments of arithmetic
Hirschfeld, J., Wheeler, W.: Forcing, arithmetic, division rings (Lect. Notes Math. 454). Berlin, Heidelberg, New York: Springer 1975
Lessan, H.: Models of arithmetic. Ph.D. thesis, University of Manchester, 1978
McAloon, K.: Completeness theorems, incompleteness theorems and models of arithmetic. Trans. Am. Math. Soc.239, 253–277 (1978)
Paris, J., Kirby, L.A.S.:ε n -Collection schemas in arithmetic. Logic Colloquium '77. Amsterdam: North-Holland, pp. 199–209, 1978
Kaye, R.: Parameter-free universal induction. Z. Math. Logik Grundlagen Math.
Paris, J.: O struktuře modelů omezenéE 1-indukce. Časopis Pěstováni Mat.109, 372–379 (1984)
Wilmers, G.: Bounded existential induction. J. Symb. Logic50, 72–90 (1985)
Author information
Authors and Affiliations
Additional information
Work on this paper was started in June 1987, while the author was visiting the University of Manchester on a British Council travel grant, and finished in the spring of 1988, while he was visiting UCLA. The author is grateful to R. Kaye, G. Wilmers and especially J. Paris for correspondence and discussions concerning this paper, and to his colleagues at UCLA for their hospitality; he also acknowledges helpful suggestions by the referees
Rights and permissions
About this article
Cite this article
Dimitracopoulos, C. Overspill and fragments of arithmetic. Arch Math Logic 28, 173–179 (1989). https://doi.org/10.1007/BF01622877
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01622877