## Abstract

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) we give a natural model of the limit law theory; and show that the limit law theory is decidable if the theory of the directly indecomposables is decidable. Using asymptotic methods from the partition calculus a useful test is derived to show several admissible classes have a first-order 0-1 law.

Original language | English (US) |
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Pages (from-to) | 641-652 |

Number of pages | 12 |

Journal | Canadian Journal of Mathematics |

Volume | 49 |

Issue number | 4 |

DOIs | |

State | Published - Aug 1997 |