## Journal of Symbolic Logic

### Decision Problem for Separated Distributive Lattices

Yuri Gurevich

#### Abstract

It is well known that for all recursively enumerable sets $X_1, X_2$ there are disjoint recursively enumerable sets $Y_1, Y_2$ such that $Y_1 \subseteq X_1, Y_2 \subseteq X_2$ and $Y_1 \cup Y_2 = X_1 \cup X_2$. 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.

#### Article information

Source
J. Symbolic Logic, Volume 48, Issue 1 (1983), 193-196.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183741204

Mathematical Reviews number (MathSciNet)
MR693262

Zentralblatt MATH identifier
0508.03016

JSTOR