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On Ehrenfeucht-Fraïssé equivalence of linear orderings

Published online by Cambridge University Press:  12 March 2014

Juha Oikkonen
Juha Oikkonen*
Affiliation:
Department of Mathematics, University of Helsinki, 00100 Helsinki, Finland
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Abstract

C. Karp has shown that if α is an ordinal with ωα = α and A is a linear ordering with a smallest element, then α and α ⊗ A are equivalent in L∞ω up to quantifer rank α. This result can be expressed in terms of Ehrenfeucht-Fraïssé games where player ∀ has to make additional moves by choosing elements of a descending sequence in α. Our aim in this paper is to prove a similar result for Ehrenfeucht-Fraïssé games of length ω1. One implication of such a result will be that a certain infinite quantifier language cannot say that a linear ordering has no descending ω1-sequences (when the alphabet contains only one binary relation symbol). Connected work is done by Hyttinen and Oikkonen in [H] and [O].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 55 , Issue 1 , March 1990 , pp. 65 - 73
Copyright
Copyright © Association for Symbolic Logic 1990

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References

REFERENCES

[B]Bonnet, R. and Pouzet, M., Linear extensions of ordered sets, Ordered sets (Rival, I., editor), Reidel, Dordrecht, 1982, pp. 125–170.CrossRefGoogle Scholar
[H]Hyttinen, T., Model theory for infinite quantifier logics, Fundament a Mathematicae (to appear).Google Scholar
[HV]Hyttinen, T. and Väänänen, J., On Scott-trees of uncountable models (to appear).Google Scholar
[K]Karp, C., Finite quantifier equivalence, The theory of models (Addison, J. W.et al., editors), North-Holland, Amsterdam, 1965, pp. 407–412.Google Scholar
[Ka]Karttunen, M., Model theory for infinitely deep languages, Annates Academiae Scientiarum Fennicae, Series A I: Mathematica. Dissertationes, no. 50 (1984).Google Scholar
[O]Oikkonen, J., How to obtain interpolation for Lκ+κ, Logic Colloquium '86 (Drake, F. and Truss, J., editors), North-Holland, Amsterdam, 1988, pp. 175–208.Google Scholar