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Abstract: The present paper characterizes classes of distributive lattices whose monadic, monadic chain, or monadic antichain theory are decidable. Mathematics Subject Classi cation (2000): 06D99, 03B25 1 Introduction The elementary theory of a nite distributive lattice can easily be interpreted in the monadic second order theory of its join irreducible elements. Therefore, the decidability of the monadic second order theory of the join irreducible elements implies that of the elementary theory of... (Update)
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BibTeX entry: (Update)
@misc{ kuske-distributive,
author = "Dietrich Kuske",
title = "Distributive Lattices With a Decidable Monadic Second Order Theory",
url = "citeseer.ist.psu.edu/kuske00distributive.html" }
Citations (may not include all citations):108 A decomposition theorem for partially ordered sets (context) - Dilworth - 1950
78 a problem of formal logic (context) - Ramsey - 1930
41 The monadic theory of order (context) - Shelah - 1975
36 Monadic second-order theories (context) - Gurevich - 1985
15 Decidability of the weak second-order theory of two successo.. (context) - Doner - 1965
5 The elementary theory of recursively enumerable sets (context) - Lachlan - 1968
5 The theory of successor with an extra predicate (context) - Thomas - 1978
4 The monadic second order logic of graphs II: Innite graphs o.. (context) - Courcelle - 1989
2 The rst order properties of algebraic systems (context) - Feferman, Vaught - 1959
1 Decision problem for separated distributive lattices (context) - Gurevich - 1983
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