Semirings of partial Boolean-valued functions arise in Bishop's approach to constructive measure theory. In this paper, we treat such semirings axiomatically. Lifting the corresponding result for Boolean rings, we prove a representation theorem a la Stone that aligns with the intended semantics. Moreover, among the semirings at hand, we determine the order of those that are free over finitely many generators.
Boolean rigs
Petrakis, Iosif
2025-01-01
Abstract
Semirings of partial Boolean-valued functions arise in Bishop's approach to constructive measure theory. In this paper, we treat such semirings axiomatically. Lifting the corresponding result for Boolean rings, we prove a representation theorem a la Stone that aligns with the intended semantics. Moreover, among the semirings at hand, we determine the order of those that are free over finitely many generators.
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