The undecidability of the lattice of r. e. closed subsets of an effective topological space (Q1098841)
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scientific article; zbMATH DE number 4037843
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The undecidability of the lattice of r. e. closed subsets of an effective topological space |
scientific article; zbMATH DE number 4037843 |
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The undecidability of the lattice of r. e. closed subsets of an effective topological space (English)
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1987
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The first-order theory of the lattice of r.e. open subsets (and hence r.e. closed subsets) of an effective topological space is shown to be undecidable. The proof uses a reduction from the theory of the lattice of r.e. sets. For the particular case of the Euclidean n-space, a more direct proof is provided, relying on a chain of two reductions, the essential one being that from the theory of symmetric, irreflexive binary relations.
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effective topological space
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