The Existence of Non-Simple Constructive Extensions of the Boolean Algebra of Clopen Sets of the Cantor Space.
IOWA UNIV IOWA CITY DEPT OF MATHEMATICS
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The theory of Boolean algebras provides a fertile framework for studying constructive extensions of computable structures. Unlike the case for fields and p-valued fields where extensions of the rationals are constructive if and only if they are computable, the present setting houses an abundance of computable extensions which are not constructive. Thus problems related to classifying or characterizing of the constructive extensions become especially interesting. The report discusses the following theorems There exist non-simple constructive extensions of the Boolean algebra of clopen sets of the Cantor space.
- Theoretical Mathematics