Fine spectra and limit laws, II first-order 0-1 laws

Stanley Burris, Kevin Compton, Andrew Odlyzko, Bruce Richmond

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

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 languageEnglish (US)
Pages (from-to)641-652
Number of pages12
JournalCanadian Journal of Mathematics
Volume49
Issue number4
DOIs
StatePublished - Aug 1997

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