Boolean algebra (structure): Difference between revisions

Revision as of 02:25, 17 September 2024

Latest revision as of 01:01, 23 August 2025

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The first axiomatization of Boolean lattices/algebras in general was given by the English philosopher and mathematician [[Alfred North Whitehead]] in 1898.{{sfn|Padmanabhan|Rudeanu|2008|p=[https://books.google.com/books?id=JlXSlpmlSv4C&pg=PA73 73]}}{{sfn|Whitehead|18981969|p=37}}

It included the [[#Definition|above axioms]] and additionally {{math|1=''x'' ∨ 1 = 1}} and {{math|1=''x'' ∧ 0 = 0}}.

In 1904, the American mathematician [[Edward V. Huntington]] (1874–1952) gave probably the most parsimonious axiomatization based on {{math|1=∧}}, {{math|1=∨}}, {{math|1=¬}}, even proving the associativity laws (see box).{{sfn|Huntington|1904|pp=292-293}}

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| doi=10.1090/s0002-9947-1936-1501865-8| doi-access=free

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*{{cite book |author-link=A.N. Whitehead |first1=A.N. |last1=Whitehead |title=A Treatise on Universal Algebra |year=1969 |publisher=Cambridge University Press |isbn=978-1-4297-0032-0 |orig-year=1898}}

*{{cite book

| author-link=A.N. Whitehead

| first1=A.N.

| last1=Whitehead

| title=A Treatise on Universal Algebra

| year=1898

| publisher=Cambridge University Press

| isbn=978-1-4297-0032-0

| url=http://projecteuclid.org/euclid.chmm/1263316509}}

=== General references ===

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}}.

*{{citation |author-link=Paul Halmos |last=Halmos |first=Paul |year=1963 |title=Lectures on Boolean Algebras |publisher=Van Nostrand}}.

*{{citation

| author-link = Paul Halmos

| last = Halmos

| first = Paul

| year = 1963

| title = Lectures on Boolean Algebras

| publisher = Van Nostrand

| isbn = 978-0-387-90094-0}}.

*{{citation

| author-link1 = Paul Halmos

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| last = Stoll

| first = R. R.

| year = 1979|orig-year=1963

| title = Set Theory and Logic

| publisher = W. H. Freeman