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EHRENFEUCHT-FRAÏSSÉ GAMES ON A CLASS OF SCATTERED LINEAR ORDERS

Published online by Cambridge University Press:  10 December 2019

FERESIANO MWESIGYE  and
JOHN KENNETH TRUSS
FERESIANO MWESIGYE
Affiliation:
DEPARTMENT OF PURE MATHEMATICS UNIVERSITY OF LEEDS LEEDS LS2 9JT, UK and DEPARTMENT OF MATHEMATICS MBARARA UNIVERSITY OF SCIENCE AND TECHNOLOGY MBARARA, P. O. BOX 1410 UGANDA E-mail:[email protected]
JOHN KENNETH TRUSS
Affiliation:
DEPARTMENT OF PURE MATHEMATICS UNIVERSITY OF LEEDS LEEDS LS2 9JT, UK E-mail:[email protected]
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Abstract

Two structures A and B are n-equivalent if Player II has a winning strategy in the n-move Ehrenfeucht-Fraïssé game on A and B. In earlier articles we studied n-equivalence classes of ordinals and coloured ordinals. In this article we similarly treat a class of scattered order-types, focussing on monomials and sums of monomials in ω and its reverse ω*.

Keywords

06A0503C64scattered linear ordermonomialEhrenfeucht-Fraïssé game
Type
Articles
Information
The Journal of Symbolic Logic , Volume 85 , Issue 1 , March 2020 , pp. 37 - 60
Copyright
Copyright © The Association for Symbolic Logic 2019 

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References

REFERENCES

Ehrenfeucht, A., An application of games to completeness problem for formalized theories. Fundamenta Mathematicae, vol. 49 (1961), pp. 129–141.CrossRefGoogle Scholar
Karp, C., Finite quantifier equivalence, The Theory of Models, Proceedings of the 1963 International Symposium at Berkeley (Addison, J. W., Henkin, L., and Tarski, A., editors), North-Holland, Amsterdam, 1965, pp. 407–412.Google Scholar
Montalban, A., Equimorphism invariants for scattered linear orderings. Fundamenta Mathematicae, vol. 191 (2006), pp.129–141.CrossRefGoogle Scholar
Mostowski, A. and Tarski, A., Arithmetically definable classes and types of well-ordered systems. Bulletin of the American Mathematical Society, vol. 55 (1949), no. 65, p. 1192.Google Scholar
Mwesigye, F., Elementary equivalence of linear orders and coloured linear orders, Ph.D. thesis, University of Leeds, 2009.Google Scholar
Mwesigye, F. and Truss, J. K., Classification of finite coloured linear orderings. Order, vol. 28 (2011), pp. 387–397.CrossRefGoogle Scholar
Mwesigye, F. and Truss, J. K., Ehrenfeucht-Fraïssé games on ordinals. Annals of Pure and Applied Logic, vol. 169 (2018), pp. 616–636.CrossRefGoogle Scholar
Mwesigye, F. and Truss, J. K., On optimal representatives of finite coloured linear orders. Order, vol. 36 (2019), pp. 107–117.CrossRefGoogle Scholar
Nadel, M., Scott sentences and admissible sets. Annals of Mathematical Logic, vol. 7 (1974), pp. 267–294.CrossRefGoogle Scholar
Rosenstein, J.G., Linear Orderings, Academic Press, New York, 1982.Google Scholar