Functional reducts of the countable atomless Boolean algebra. (English) Zbl 1532.03050
\(A\) is a functional reduct of \(B\) iff the fundamental operations of \(A\) are terms of \(B\). \(A\) is equivalent to \(B\) iff their groups of automorphisms are the same. It is shown that there are exactly 13 functional reducts of the countable atomless Boolean algebra up to equivalence.
Reviewer: James Monk (Boulder)
MSC:
| 03C40 | Interpolation, preservation, definability |
| 06E05 | Structure theory of Boolean algebras |
| 06E25 | Boolean algebras with additional operations (diagonalizable algebras, etc.) |
| 06E30 | Boolean functions |
| 20B35 | Subgroups of symmetric groups |
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