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Decision problem for separated distributive lattices

Published online by Cambridge University Press:  12 March 2014

Yuri Gurevich
Yuri Gurevich*
Affiliation:
Ben-Gurion University, Beer Sheva, Israel
*
University of Michigan, Ann Arbor, Michigan 48104
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Abstract

It is well known that for all recursively enumerable sets X1, X2 there are disjoint recursively enumerable sets Y1 ⊆ Y2 such that Y ⊆ X1, Y2 ⊆ X2 and Y1, ⋃ Y2 = X1 ⋃ X2. Alistair Lachlan called distributive lattices satisfying this property separated. He proved that the first-order theory of finite separated distributive lattices is decidable. We prove here that the first-order theory of all separated distributive lattices is undecidable.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 48 , Issue 1 , March 1983 , pp. 193 - 196
Copyright
Copyright © Association for Symbolic Logic 1983

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References

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