Decision problem for separated distributive lattices

Journal of Symbolic Logic 48 (1):193-196 (1983)
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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 ∪ Y 2 = X 1 ∪ 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

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The∀∃ theory of Peano Σ1 sentences.Per Lindström & V. Yu Shavrukov - 2008 - Journal of Mathematical Logic 8 (2):251-280.

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