Using Feferman-Vaught techniques a condition on the fine spectrum of an admissible class of structures is found which leads to a first-order 0--1 law. The condition presented is best possible in the sense that if it is violated then one can find an admissible class with the same fine spectrum which does not have a first-order 0--1 law. If the condition is satisfied (and hence we have a first-order %% 0--1 law)

MSC Classifications:

03N45, 11N45, 11N80, 05A15, 05A16, 11M41, 11P81 show english descriptions unknown classification 03N45
Asymptotic results on counting functions for algebraic and topological structures
Generalized primes and integers
Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]
Asymptotic enumeration
Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72}
Elementary theory of partitions [See also 05A17] 03N45 - unknown classification 03N45
11N45 - Asymptotic results on counting functions for algebraic and topological structures
11N80 - Generalized primes and integers
05A15 - Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]
05A16 - Asymptotic enumeration
11M41 - Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72}
11P81 - Elementary theory of partitions [See also 05A17]

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