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SUMMARY:Marcel Jackson (La Trobe University Melbourne\, Australia)
DTSTART:20211019T190000Z
DTEND:20211019T200000Z
DTSTAMP:20260423T004131Z
UID:PALS/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PALS/14/">Un
 decidability of representability as binary relations</a>\nby Marcel Jackso
 n (La Trobe University Melbourne\, Australia) as part of PALS Panglobal Al
 gebra and Logic Seminar\n\n\nAbstract\nIt is well-known and easy to prove 
 that the variety of groups abstractly captures algebras of permutations un
 der composition and inverse\, that the variety of inverse semigroups captu
 re algebras of partial injective functions under composition and inverse\,
  and that the variety of semigroups abstractly capture the algebras of any
  of total functions\, partial functions or binary relations under the oper
 ation of composition.  In contrast to this\, a landmark result of Hirsch a
 nd Hodkinson showing the undecidability of determining when a finite algeb
 ra is isomorphic to an algebra of binary relations under Tarski’s signat
 ure: the usual set theoretic Boolean operations\, composition\, converse a
 nd identity.  This is a very rich signature\, and it has subsequently been
  discovered that undecidability of representability begins in weaker signa
 tures.\n\nThis talk will survey some of the very extensive literature in t
 his area\, and an overview of the approaches to undecidability\, possibly 
 touching on some new results for one of the weakest known algebraic signat
 ure to experience undecidability of representability as binary relations.\
 n
LOCATION:https://researchseminars.org/talk/PALS/14/
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