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On sets of relations definable by addition

Published online by Cambridge University Press:  12 March 2014

James F. Lynch
James F. Lynch*
Affiliation:
Clarkson College of Technology, Potsdam, New York 13676
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Abstract

For every κ ∈ ω, there is an infinite set Aκ ⊆ ω and a d(κ) ∈ ω such that for all Q0, Q1, ⊆ Aκ where ∣Q0∣ = ∣ Q1∣, or d(κ) < ∣Q0∣, Q1∣ < ℵ0, the structures ‹ω, +, Q0› and ‹ω, +, Q1› are indistinguishable by first-order sentences of quantifier depth κ whose atomic formulas are of the form u = v, u + v = w, and Q(u), where u, v, and w are variables.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 47 , Issue 3 , September 1982 , pp. 659 - 668
Copyright
Copyright © Association for Symbolic Logic 1982

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References

REFERENCES

[1] Benda, M., Infinite words as universes (to appear).Google Scholar
[2] Büchi, J. R., Weak second-order arithmetic and finite automata, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 6 (1960), pp. 66–92.CrossRefGoogle Scholar
[3] Ehrenfeucht, A. and Mostowski, A., Models of axiomatic theories admitting automorphisms, Fundament a Mathematicae, vol. 43 (1957), pp. 50–68.CrossRefGoogle Scholar
[4] Ehrenfeucht, A., An application of games to the completeness problem for formalized theories, Fundament a Mathematicae, vol. 49 (1961), pp. 129–141.CrossRefGoogle Scholar
[5] Elgot, C.C., Decision problems of finite-automata design and related arithmetics, Transactions of the American Mathematical Society, vol. 98 (1961), pp. 21–51.CrossRefGoogle Scholar
[6] Fagin, R., Generalized first-order spectra and polynomial-time recognizable sets, Complexity of computation (Karp, R.M., Editor), American Mathematical Society, Providence, RI, 1974, pp. 43–73.Google Scholar
[7] Fagin, R., Monadic generalized spectra, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 21 (1975), pp. 89–96.CrossRefGoogle Scholar
[8] Fagin, R., Probabilities on finite models, this Journal, vol. 41 (1976), pp. 50–58.Google Scholar
[9] Gaifman, H., Concerning measures in first-order calculi, Israel Journal of Mathematics, vol. 2(1964), pp. 1–17.CrossRefGoogle Scholar
[10] Immerman, N., Number of quantifiers is better than number of tape cells, Journal of Computer and Systems Sciences (to appear).Google Scholar
[11] Jones, N. D. and Selman, A. L., Turing machines and the spectra of first-order formulas with equality, this Journal, vol. 39 (1974), pp. 139–150.Google Scholar
[12] Lynch, J. F., Almost sure theories, Annals of Mathematical Logic, vol. 18 (1980), pp. 91–135.CrossRefGoogle Scholar
[13] Lynch, J. F., Complexity classes and theories of finite models, Mathematical Systems Theory (to appear).Google Scholar
[14] Makkai, M. and Mycielski, J., An Lω1ω complete and consistent theory without models, Proceedings of the American Mathematical Society, vol. 62 (1977), pp. 131–133.Google Scholar
[15] Mckenzie, R., Mycielski, J. and Thompson, D., On boolean functions and connected sets, Mathematical Systems Theory, vol. 5 (1971), pp. 259–270.CrossRefGoogle Scholar
[16] Monk, J. D., Mathematical logic, Springer-Verlag, New York, 1976.CrossRefGoogle Scholar
[17] Rabin, M. O., Decidability of second-order theories and automata on infinite trees, Transactions of the American Mathematical Society, vol. 141 (1969), pp. 1–35.Google Scholar
[18] Reyes, G. E., Local definability theory, Annals of Mathematical Logic, vol. 1 (1970), pp. 95–137.CrossRefGoogle Scholar
[19] Robinson, J., Definability and decision problems in arithmetics, this Journal, vol. 14 (1949), pp. 98–114.Google Scholar