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Stratified languages

Published online by Cambridge University Press:  12 March 2014

A. Pétry
A. Pétry*
Affiliation:
Institut Supérieur, Industriel Liégeois, B 4020 Liège, Belgium
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Abstract

We consider arbitrary stratified languages. We study structures which satisfy the same stratified sentences and we obtain an extension of Keisler's Isomorphism Theorem to this situation. Then we consider operations which are definable by a stratified formula and modify the ‘type’ of their argument by one; we prove that for such an operation F the sentence c = F(c) and the scheme φ(c) ↔ (F(c)), where ↔(x) varies among all the stratified formulas with no variable other than x free, imply the same stratified {c}-sentences.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 57 , Issue 4 , December 1992 , pp. 1366 - 1376
Copyright
Copyright © Association for Symbolic Logic 1992

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References

REFERENCES

[1]Bernays, P., A system of axiomatic set theory, part VII, this Journal, vol. 19 (1954), pp. 81–91.Google Scholar
[2]Boffa, M., Stratified formulas in Zermelo-Fraenkel set theory, Bulletin de l'Academiepolonaise des Sciences, Série Math., vol. 19 (1971), pp. 275–280.Google Scholar
[3]Chang, C. C. and Keisler, H. J., Model theory (third edition), North-Holland, Amsterdam, 1990.Google Scholar
[4]Crabbé, M., Ambiguity and stratification, Fundamenta Mathematicae, vol. 101 (1978), pp. 11–17.CrossRefGoogle Scholar
[5]Forster, T., Permutations and stratified formulae a preservation theorem, Zeitschrift für Mathematische Logik undGrundlagen der Mathematik, vol. 36 (1990), pp. 385–388.CrossRefGoogle Scholar
[6]Henson, C. W., Finite sets in Quine's New Foundations, this Journal, vol. 34 (1969), pp. 589–596.Google Scholar
[7]Henson, C. W., Permutations method applied to Quine's New Foundations, this Journal, vol. 38 (1973), pp. 69–76.Google Scholar
[8]Pétry, A., Une caractérisation algébrique des structures satisfaisant les mémes sentences stratifiées, La Théorie des ensembles de Quine, Cahiers du Centre de Logique, vol. 4, Louvain-la Neuve, pp. 7–16.Google Scholar
[9]Quine, W. v. O., New foundations for mathematical logic, American Mathematical Monthly, vol. 44 (1937), pp. 70–80.CrossRefGoogle Scholar
[10]Rieger, L., A contribution to Gödel's axiomatic set theory, Czechoslovak Mathematical Journal, vol. 7 (1957), pp. 323–357.CrossRefGoogle Scholar
[11]Scott, D., Quine's individuals, Logic, methodology and philosophy of Science (Nagel, E.et. al., editors), Stanford University Press, Stanford, CA, 1962, pp. 111–115.Google Scholar
[12]Shelah, S., Every two elementary equivalents models have isomorphic ultrapowers, Israel Journal of Mathematics, vol. 10 (1972), pp. 224–233.CrossRefGoogle Scholar
[13]Specker, E. P., Typical ambiguity, Logic, methodology and philosophy of Science (Nagel, E.et al., editors), Stanford University Press, Stanford, CA, 1962, pp. 116–124.Google Scholar