### Spectra of monadic second order sentences

by Shelah. [Sh:817]

Scientiae Math Japonicae, 2004

For a monadic sentence psi in the finite vocabulary we show
that the spectra, the set of cardinalities of models of psi is
almost periodic under reasonable conditions. The first is that
every model is so called ``weakly k-decomposable''. The second is
that we restrict ourselves to a nice class of models constructed by
some recursion.

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