| Lindenbaum-tarski Algebra |
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Information AboutLindenbaum-tarski Algebra |
| CATEGORIES ABOUT LINDENBAUM–TARSKI ALGEBRA | |
| mathematical logic | |
p That is, in ''T'' the sentence ''q'' can be deduced from ''p'', and ''p'' from ''q''. Operations in ''A'' are inherited from those available in ''T'', typically Conjunction and Disjunction , where they are Well-defined on the classes. When Negation is present in ''T'', then ''A'' is a Boolean Algebra , under some mild conditions. Conversely, for every Boolean algebra ''A'', there is a theory ''T'' of (classical) Sentential Logic such that the Lindenbaum-Tarski algebra of ''T'' is Isomorphic to ''A''. In other words, every Boolean algebra is (up to isomorphism) a Lindenbaum-Tarski algebra. Sometimes called simply Lindenbaum algebra, this construction is named for Logician s Adolf Lindenbaum and Alfred Tarski . SEE ALSO |
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