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DTSTART;TZID=America/Toronto:20240131T143000
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URL:https://uwaterloo.ca/pure-mathematics/events/logic-seminar-57
SUMMARY:Logic Seminar
CLASS:PUBLIC
DESCRIPTION:ROSS WILLARD\, UNIVERSITY OF WATERLOO\n\n\"RESIDUALLY FINITE EQ
 UATIONAL THEORIES\"\n\nAn equational theory T is said to be residually fin
 ite if every model\nof the theory can be embedded in a product of finite m
 odels of the\ntheory.  Equivalently\, T is residually finite if and only 
 if its\nirreducible models (those that cannot be embedded in products of\n
 “simpler” models) are all finite.  In practice\, it seems that\nwhene
 ver a theory is both “interesting” and residually finite\,\nthen there
  is a finite upper bound to the sizes of its irreducible\nmodels.  In oth
 er words\, we see a sort of compactness principle for\n“interesting” e
 quational theories: if such a theory has\narbitrarily large finite irreduc
 ible models\, then it must have an\ninfinite irreducible model.  Whether 
 or not this observation holds\ngenerally has been open for almost 50 years
 .  In this talk I will\ndiscuss some recent progress with collaborators K
 eith Kearnes and\nAgnes Szendrei.\n\nMC 5479
DTSTAMP:20260506T091642Z
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