By Vadim G. Korneev, Ulrich Langer
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P map in If is an are the repre- are the T °p natural can be e m b e d d e d W are both is a p r e d i c a t e Let P A in have it is a full which X UA for every such A. definition of HT The and will and equivalences. H~, then domain P X. is a m o n i c Then Up. ,Zn)) M ~+m f > M are both in and J. M ~+n Let be the diagram: M~+m+n P~+_~n > M~+n P~+m M~+m > M f Then V(H X) then ~ > M. X represents U A. limit of such that is s t r a i g h t f o r w a r d from the embedding. is a c o n j u n c t i o n X 6 0b(~) give the represents V(HX) represents (2) Hence for every there It follows and ~.
T h e connections between elementary theories and polyadic algebras have been studied by Daigneault in . In this paper w e will prove the completeness t h e o r e m for elementary theories, suggested by Z a w v e r e in [141 . T h e proof is categorical, but it can be said that it follows, in a sense, the lines of the completeness proof in Henkin [81o W e will use the slightly m o r e logical category. general notion of a Aside f r o m having s o m e technical advantages, this permits an extension of the results to higher order logic.
A functor from finitely cocontinuous and finitely continuous. Also J2 R' in S T(M 2) = M 1. (Y2) is monic in > S(Y2 ) ~pn C it follows that is T is y 6~ 2 is monic, then R'(H y) Hy is an onto map is onto. Hence T(y) Yi" T: Y2 To show that lent in J~P. 4 implies that Therefore respect If Jl" is cocontinuous R'(H M2 ) Therefore to S T = Q' This to direct > J1 follows limits in is a Horn theory map. D. and both functors with preserve direct limits. D. Similarly following with respect one can show that diagram commutes.
Approximate solution of plastic flow theory problems by Vadim G. Korneev, Ulrich Langer