A DIRECTLY REPRESENTABLE VARIETY HAS A DISCRETE FIRST-ORDER LAW

Author:

BURRIS STANLEY1,IDZIAK PAWEL2

Affiliation:

1. Dept. of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

2. Dept. of Computer Science, Jagiellonian University, Cracow, Poland

Abstract

Using simple counting arguments, the Feferman-Vaught techniques and selected results from universal algebra, we show that for any directly representable variety V there is a positive integer k such that for any first-order sentence ϕ the proportion of members of V of size at most x which satisfy ϕ tends to a limit belonging to [Formula: see text] as x goes to infinity. Furthermore there is a first-order statement for which the limit is [Formula: see text]. V has a 0–1 law (i.e., k=1) iff the finite members factor uniquely into directly indecomposables.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. ABSTRACT NUMBER SYSTEMS AND LOGICAL LIMIT LAWS;Quaestiones Mathematicae;2001-09

2. COUNTING FINITE ALGEBRAS IN THE POST VARIETIES;International Journal of Algebra and Computation;2000-06

3. Classification in finite model theory: counting finite algebras;Structural Theory of Automata, Semigroups, and Universal Algebra

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