Partial Boolean algebras in a broader sense |
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Authors: | Janusz Czelakowski |
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Institution: | (1) The Section of Logic, Polish Academy of Sciences Institute of Philosophy and Sociology, Poland |
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Abstract: | The article deals with compatible families of Boolean algebras. We define the notion of a partial Boolean algebra in a broader sense (PBA(bs)) and then we show that there is a mutual correspondence between PBA(bs) and compatible families of Boolean algebras (Theorem (1.8)). We examine in detail the interdependence between PBA(bs) and the following classes: partial Boolean algebras in the sense of Kochen and Specker (§ 2), ortholattices (§ 3, § 5), and orthomodular posets (§ 4), respectively. |
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