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@article{1502260, author = {Almeida, Jorge and Klíma, Ondřej}, article_location = {Lisboa}, article_number = {2}, doi = {http://dx.doi.org/10.4171/PM/2012}, keywords = {Pseudoidentity; syntactical proof; semigroup; profinite monoid; completeness; reducible pseudovariety; implicit signature}, language = {eng}, issn = {0032-5155}, journal = {Portugaliae mathematica}, title = {Towards a pseudoequational proof theory}, volume = {75}, year = {2018} }
TY - JOUR ID - 1502260 AU - Almeida, Jorge - Klíma, Ondřej PY - 2018 TI - Towards a pseudoequational proof theory JF - Portugaliae mathematica VL - 75 IS - 2 SP - 79-119 EP - 79-119 SN - 00325155 KW - Pseudoidentity KW - syntactical proof KW - semigroup KW - profinite monoid KW - completeness KW - reducible pseudovariety KW - implicit signature N2 - A new scheme for proving pseudoidentities from a given set Sigma of pseudoidentities, which is clearly sound, is also shown to be complete in many instances, such as when Sigma defines a locally finite variety, a pseudovariety of groups, more generally, of completely simple semigroups, or of commutative monoids. Many further examples for which the scheme is complete are given when Sigma defines a pseudovariety V which is sigma-reducible for the equation x=y, provided Sigma is enough to prove a basis of identities for the variety of sigma-algebras generated by V. This gives ample evidence in support of the conjecture that the proof scheme is complete in general. ER -
ALMEIDA, Jorge a Ondřej KLÍMA. Towards a pseudoequational proof theory. \textit{Portugaliae mathematica}. Lisboa, roč.~75, č.~2, s.~79-119. ISSN~0032-5155. doi:10.4171/PM/2012. 2018.
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