Vol. 32, No. 3, 1970

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Extending Boolean operations

Leon A. Henkin

Vol. 32 (1970), No. 3, 723–752

The Stone representation theory provides a canonical method whereby each Boolean algebra A can be embedded isomorphically in a complete, atomistic Boolean algebra A. Jonsson and Tarski have shown how each additive operation (of any number of places) on A can be extended canonically to a completely additive operation on A, in such a way that whenever an equation involving given additive operations holds identically in A, the corresponding equation involving the canonical extensions of those operations will hold identically in A. In this paper we present a generalization of this result.

Mathematical Subject Classification
Primary: 06.60
Received: 2 August 1969
Published: 1 March 1970
Leon A. Henkin