Talk:MV-algebra

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This article may be too technical for most readers to understand, and needs attention from an expert on its subject. Please expand it to make it accessible to non-experts, without removing the technical details.

In my opinion, the above banner is over the top. I am wholly self taught in logic and algebra, and do NOT find this entry unusually challenging. True, a residuated lattice is not an easy concept, but there is no need to grasp it in order to understand what an MV algebra is. An MV algebra is a flavour of commutative monoid, near-baby talk, mathematically speaking

Unrelated question. Is x \oplus \lnot x = 0 or 1 an MV algebra theorem? If yes, MV algebras are well connected either to groups or to Boolean algebras.202.36.179.65 22:37, 17 August 2006 (UTC)

[edit] Wrong Wrong Wrong Wrong Wrong!

There are many errors in this article.

MV algebras were not invented by Jan Łukasiewicz, but by Chang.

Chang's Completeness Theorem is that Łukasiewicz logic is complete for MV algebras.

Change's Representation Theorem is that all MV algebras are isomorphic to the subdirect product of two linear MV algebras.

Identities which hold in a linear MV algebra will hold in (sub)direct product of that linear algebra.

Chang also proved (1959) that any identity in the MV algebra R[1] (an MV algebra for the interval [0,1]) is an identity for any linear MV algebra.

Hence identities in R[1] hold for all MV algebras.

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