Live briefing
Everything about Free Boolean algebra
Boolean algebra generated by a set with no relations beyond Boolean laws
In mathematics, a free Boolean algebra is a Boolean algebra with a distinguished set of elements, called generators, such that:Each element of the Boolean algebra can be expressed as a finite combination of generators, using the Boolean operations, and The generators are as independent as possible, in the sense that there are no relationships among them that do not hold in every Boolean algebra no matter which elements are chosen. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Free Boolean algebraA 5-minute orientation
- Skim a recent paper: Boolean Algebras with Semigroup Operators: Free Product and Free ObjectsInfluential work since 2022
- Pick up a classic book: Mathematical structures for computer scienceThe most-reprinted book on the subject
- Read the landmark paper: Monotone, free, and boolean cumulants: A shuffle algebra approachCited 14 times
- Go sideways: Complete Boolean algebraA closely related topic
- Go sideways: Cardinal functionA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Monotone, free, and boolean cumulants: A shuffle algebra approach
A model of ZF with an infinite free complete Boolean algebra
🆕 Influential since 2022
đź“š Books worth reading
Mathematical structures for computer scienceJudith L. Gersting · 1982
Language and Automata Theory and ApplicationsAdrian-Horia Dediu · 2012
Introduction to automata theory, languages, and computationJohn E. Hopcroft, Jeffrey D. Ullman · 1979
Physics for computer science studentsNarciso Garcia · 1986
Snow mountain passageJames D. Houston · 2001
Principles of compiler designAlfred V. Aho, Jeffrey D. Ullman · 1977
AQA A-Level Computer ScienceBob Reeves · 2015
Foundations of computer scienceAlfred V. Aho · 1992
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
- Complete Boolean algebra In mathematics, a complete Boolean algebra is a Boolean algebra in which every subset has a supremum (least upper bound). Complete Boolean algebras are…
- Cardinal function In mathematics, a cardinal function (or cardinal invariant) is a function that returns cardinal numbers. The most frequently used cardinal function is…
- Power set In mathematics, the power set (or powerset) of a set S is the set of all subsets of S, including the empty set and S itself. In axiomatic set theory (as…
- Boolean algebra (structure) In mathematics, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties…
- Free lattice In mathematics, in the area of order theory, a free lattice is the free object corresponding to a lattice. As free objects, they have the universal property…
- Infinitary combinatorics In mathematics, infinitary combinatorics, or combinatorial set theory, is an extension of ideas in combinatorics to infinite sets. Some of the things studied…
- Free group In mathematics, the free group F S {\displaystyle F_{S}} over a given set S {\displaystyle S} consists of all words that can be built from members of S…
- Glossary of module theory Module theory is the branch of mathematics in which modules are studied. This is a glossary of some terms of the subject. See also: Glossary of linear…