Relational structures constructible by quantifier free definable operations

by Doron and Shelah. [DoSh:865]
J Symbolic Logic, 2007
We consider three classes of models: models of bounded patch width defined Fisher and Makowsky, models constructible by addition operations that preserve monadic theories defined in [Sh:817], and models monadicaly interpretable in trees defined below. For all three classes we have eventual periodicity of restricted spectrum of MSO sentences. We show that the second and third classes are in some sence equivalent, while the first is essentially smaller.

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