Annals of Pure and Applied Logic 35 (2):193-203 (1987)

Abstract
The first-order theory of the lattice of recursively enumerable closed subsets of an effective topological space is proved undecidable using the undecidability of the first-order theory of the lattice of recursively enumerable sets. In particular, the first-order theory of the lattice of recursively enumerable closed subsets of Euclidean n -space, for all n , is undecidable. A more direct proof of the undecidability of the lattice of recursively enumerable closed subsets of Euclidean n -space, n ⩾ 2, is provided using the method of reduction and the recursive inseparability of the set of all formulae satisfiable in every model of the theory of SIBs and the set of all formulae refutable in some finite model of the theory of SIBs
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DOI 10.1016/0168-0072(87)90063-7
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References found in this work BETA

A Survey of Lattices of Re Substructures.Anil Nerode & Jeffrey Remmel - 1985 - In Anil Nerode & Richard A. Shore (eds.), Recursion Theory. American Mathematical Society. pp. 42--323.
Simplicity in Effective Topology.Iraj Kalantari & Anne Leggett - 1982 - Journal of Symbolic Logic 47 (1):169-183.
Undecidability of Some Topological Theories.Andrzej Grzegorczyk - 1953 - Journal of Symbolic Logic 18 (1):73-74.

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