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Overlap Algebras: a Constructive Look at Complete Boolean Algebras [PDF]
Logical Methods in Computer Science, 2020 The notion of a complete Boolean algebra, although completely legitimate in constructive mathematics, fails to capture some natural structures such as the lattice of subsets of a given set.
Francesco Ciraulo, Michele Contente
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Not all 𝜎-complete Boolean algebras are quotients of complete Boolean algebras [PDF]
Proceedings of the American Mathematical Society, 1992 In Shelah’s model of no Borel lifting of the measure algebra we show that there is a σ \sigma
Dow, A., Vermeer, J.
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Simple complete Boolean algebras [PDF]
Israel Journal of Mathematics, 1974 IfV=L, and κ is an uncountable regular non weakly compact cardinal, then there exists a simple complete Boolean algebra of cardinality κ.
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The three types of normal sequential effect algebras [PDF]
Quantum, 2020 A sequential effect algebra (SEA) is an effect algebra equipped with a $\textit{sequential product}$ operation modeled after the Lüders product $(a,b)\mapsto \sqrt{a}b\sqrt{a}$ on C$^*$-algebras.
Abraham Westerbaan +2 more
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A Category of Ordered Algebras Equivalent to the Category of Multialgebras
Bulletin of the Section of Logic, 2023 It is well known that there is a correspondence between sets and complete, atomic Boolean algebras (\(\textit{CABA}\)s) taking a set to its power-set and, conversely, a complete, atomic Boolean algebra to its set of atomic elements.
Marcelo Esteban Coniglio +1 more
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The prime state ideal theorem in state residuated lattices [PDF]
Categories and General Algebraic Structures with Applications, 2023 The aim of this paper is to establish the prime state ideal theorem in state residuated lattices (SRLs). We study the state ideals lattice $\mathcal{SI}(L)$ of astate residuated lattice $(L, \varphi)$ andprove that it is a complete Brouwerian lattice ...
Francis Woumfo +2 more
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L-Fuzzy Prime Spectrums of ADLs
Advances in Fuzzy Systems, 2021 The notion of an Almost Distributive Lattice (ADL) is a common abstraction of several lattice theoretic and ring theoretic generalizations of Boolean algebra and Boolean rings.
Natnael Teshale Amare +2 more
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P-Fuzzy Ideals and P-Fuzzy Filters in P-Algebras
Advances in Fuzzy Systems, 2021 In this paper, we introduce the concept of p-fuzzy ideals and p-fuzzy filters in a p-algebra. We provide a set of equivalent conditions for a fuzzy ideal to be a p-fuzzy ideal and a p-algebra to be a Boolean algebra.
Wondwosen Zemene Norahun
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Rough Approximation Operators on a Complete Orthomodular Lattice
Axioms, 2021 This paper studies rough approximation via join and meet on a complete orthomodular lattice. Different from Boolean algebra, the distributive law of join over meet does not hold in orthomodular lattices. Some properties of rough approximation rely on the
Songsong Dai
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On the Complexity of the Evaluation of Transient Extensions of Boolean Functions [PDF]
Electronic Proceedings in Theoretical Computer Science, 2010 Transient algebra is a multi-valued algebra for hazard detection in gate circuits. Sequences of alternating 0's and 1's, called transients, represent signal values, and gates are modeled by extensions of boolean functions to transients.
Janusz Brzozowski, Baiyu Li, Yuli Ye
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