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Ranked partial structures

Published online by Cambridge University Press:  12 March 2014

Timothy J. Carlson
Timothy J. Carlson*
Affiliation:
Department of Mathematics, Ohio State University, Columbus, OH 43210, USA, E-mail: carlson@math.ohio-state.edu
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Abstract

The theory of ranked partial structures allows a reinterpretation of several of the standard results of model theory and first-order logic and is intended to provide a proof-theoretic method which allows for the intuitions of model theory. A version of the downward Löwenheim-Skolem theorem is central to our development. In this paper we will present the basic theory of ranked partial structures and their logic including an appropriate version of the completeness theorem.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 4 , December 2003 , pp. 1109 - 1144
Copyright
Copyright © Association for Symbolic Logic 2003

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References

REFERENCES

[1] Beeson, M., Foundations of constructive mathematics, Springer-Verlag, 1985.CrossRefGoogle Scholar
[2] Ketonen, J. and Solovay, R. M., Rapidly growing Ramsey functions, Annals of Mathematics, vol. 113 (1981), pp. 267–314.CrossRefGoogle Scholar
[3] Kirby, L. A. S. and Paris, J. B., Accessible independence results for Peano arithmetic, Bulletin of the London Mathematical Society, vol. 14 (1982), pp. 285–293.CrossRefGoogle Scholar
[4] Mills, G., A tree analysis of unprovable combinatorial statements, Model theory of algebra and arithmetic, Lecture Notes in Mathematics, vol. 834, Springer-Verlag, 1980, pp. 248–311.CrossRefGoogle Scholar
[5] Mycielski, J., Locally finite theories, this Journal, vol. 51 (1986), pp. 59–62.Google Scholar
[6] Paris, J. and Harrington, L., A mathematical incompleteness in Peano arithmetic, Handbook of mathematical logic (Barwise, J., editor), North Holland, 1977, pp. 1133–1142.CrossRefGoogle Scholar
[7] Quinsey, J. E., Some problems in logic, Ph.D. thesis , St. Catherine's College, Oxford, 04 1980.Google Scholar
[8] Silver, J., mimeographed notes.Google Scholar
[9] Skolem, T., Über die mathematische Logik, Norsk Matematisk Tidsskrift, vol. 10 (1928), pp. 125–142.Google Scholar
[10] van Heijenoort, J. (editor), From Frege to Gödel. A source book in mathematical logic, Harvard University Press, Cambridge, 1967.Google Scholar