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Relational structures constructible by quantifier free definable operations

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah
Affiliation:
The Hebrew University of Jerusalem, Einstein Institute of Mathematics, Edmond Safra Campus, Givat Ram, Jerusalem 91904, Israel. E-mail: shelah@math.huji.ac.il
Mor Doron
Affiliation:
The Hebrew University of Jerusalem, Einstein Institute of Mathematics, Edmond Safra Campus, Givat Ram, Jerusalem 91904, Israel. E-mail: mord@math.huji.ac.il

Abstract

We consider the notion of bounded m-ary patch-width defined in [9], and its very close relative m-constructibility defined below. We show that the notions of m-constructibility all coincide for m ≥ 3, while 1-constructibility is a weaker notion. The same holds for bounded m-ary patch-width. The case m = 2 is left open.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2007

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References

[1]Asser, G., Das Repräsentantenproblem im Prädikatenkalkül der ersten Stufe mit Identität, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 1 (1955), pp. 252263.CrossRefGoogle Scholar
[2]Blumensath, A., Axiomatising tree-interpretable structures, Theory of Computing Systems, vol. 237 (2004), no. 1, pp. 327.CrossRefGoogle Scholar
[3]Blumensath, A. and Courcelle, B., Recognizability, hypergraph operations, and logical types, Information and Computation, vol. 204 (2006), no. 6, pp. 853919.CrossRefGoogle Scholar
[4]Courcelle, B., The monadic second order logic of graphs. VII. Graphs as relational structures. Theoretical Computer Science, vol. 101 (1992), no. 1, pp. 333.CrossRefGoogle Scholar
[5]Courcelle, B., Monadic second-order definable graph transductions: a survey, Theoretical Computer Science, vol. 126 (1994), no. 1, pp. 5375.CrossRefGoogle Scholar
[6]Courcelle, B., Structural properties of context-free sets of graphs generated by vertex replacement, Information and Computation, vol. 116 (1995), no. 2, pp. 275293.CrossRefGoogle Scholar
[7]Durand, A., Fagin, R., and Loescher, B., Spectra with only unary function symbols. Computer science logic (Aarhus, 1997), Lecture Notes in Computer Science, vol. 1414, Springer, Berlin, 1998, pp. 189202.CrossRefGoogle Scholar
[8]Ebbinghaus, H. D. and Flum, J., Finite model theory, second ed., Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1999.Google Scholar
[9]Fischer, E. and Makowsky, J. A., On spectra of sentences of monadic second order logic with counting, this Journal, vol. 69 (2004), no. 3, pp. 617640.Google Scholar
[10]Gurevich, Y. and Shelah, S., Spectra of monadic second-order formulas with one nary function, LICS '03, IEEE Computer Society, 2003, pp. 291300.Google Scholar
[11]Shelah, S., Spectra of monadic second order sentences, Scientiae Mathematicae Japonicae, vol. 59 (2004), no. 2, pp. 351355, Special issue on set theory and algebraic model theory.Google Scholar

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