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**1 - 2**of**2**### Spectra and Systems of Equations

- CONTEMPORARY MATHEMATICS

"... Periodicity properties of sets of nonnegative integers, defined by systems Y = G(Y) of equations, are analyzed. Such systems of set equations arise naturally from equational specifications of combinatorial classes— Compton’s equational specification of monadic second order classes of trees is an i ..."

Abstract
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Periodicity properties of sets of nonnegative integers, defined by systems Y = G(Y) of equations, are analyzed. Such systems of set equations arise naturally from equational specifications of combinatorial classes— Compton’s equational specification of monadic second order classes of trees is an important example. In addition to the general theory of set equations and periodicity, with several small illustrative examples, two applications are given: (1) There is a new proof of the fundamental result of Gurevich and Shelah on the periodicity of monadic second order classes of finite monounary algebras. Also there is a new proof that the monadic second order theory of finite monounary algebras is decidable. (2) A formula derived for the periodicity parameter q is used in the determination of the asymptotics for the coefficients of generating functions defined by well conditioned systems of equations.