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Everything about Complete Boolean algebra
Boolean algebra with all operators and laws forming a complete logical system
In mathematics, a complete Boolean algebra is a Boolean algebra in which every subset has a supremum. Complete Boolean algebras are used to construct Boolean-valued models of set theory in the theory of forcing. Every Boolean algebra A has an essentially unique completion, which is a complete Boolean algebra containing A such that every element is the supremum of some subset of A. As a partially ordered set, this completion of A is the Dedekind–MacNeille completion. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Complete Boolean algebraA 5-minute orientation
- Skim a recent paper: Output Stabilizing Control of Complex Biological Networks Based on Boolean Algebra AnalysisInfluential work since 2022
- Pick up a classic book: Slozhnostʹ zadachi razbieni͡ia mnozhestva nuleĭ bulevoĭ funk͡tsii na nepereseka͡iushchies͡ia podmnozhestvaThe most-reprinted book on the subject
- Read the landmark paper: The uniformly closed algebra generated by a complete Boolean algebra of projectionsCited 8 times
- Go sideways: Glossary of set theoryA closely related topic
- Go sideways: Power setA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
The uniformly closed algebra generated by a complete Boolean algebra of projections
A complete Boolean algebra of subspaces which is not reflexive
The Jacobson Algebras and Boolean Algebras in Normal Classes of Pointwise Complete Algebra
Postulates for Boolean Algebra Involving the Operation of Complete Disjunction
Boolean-valued equivalence relations and complete extensions of complete boolean algebras
A Complete Boolean Algebra That Has No Proper Atomless Complete Subalgebra
A countably distributive complete Boolean algebra not uncountably representable
On the commutant of a complete Boolean algebra of projections
🆕 Influential since 2022
📚 Books worth reading
- 📕Slozhnostʹ zadachi razbieni͡ia mnozhestva nuleĭ bulevoĭ funk͡tsii na nepereseka͡iushchies͡ia podmnozhestvaK. V. Zado͡ian · 1988
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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