Complete Representations and Neat Embeddings

Complete Representations and Neat Embeddings

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Let (2Dab Rigs algebras of dimension (n), ({sf RCA}_n) denotes the class of representable (sf CA_n)s, ({sf CRCA}_n) denotes the class of completely representable ({sf CA}_n)s, and ({sf Nr}_n{sf CA}_{omega}(subseteq {sf CA}_n)) denotes the class of (n)-neat reducts of ({sf CA}_{omega})s.The elementary closure of the class ({sf CRCA}_n)s ((mathbf{K_n})) and the non-elementary class ({sf At}({sf Nr}_n{sf CA}_{omega})) are characterized using two-player zero-sum games, where ({sf At}) is the operator of forming atom structures.It is shown that (mathbf{K_n}) is not finitely axiomatizable and that it coincides with the class of atomic algebras in the elementary closure of (mathbf{S_c}{sf Nr}_n{sf CA}_{omega}) where (mathbf{S_c}) is the operation of forming complete subalgebras.For any class (mathbf{L}) such that ({sf At}{sf Nr}_n{sf CA}_{omega}subseteq mathbf{L}subseteq {sf At}mathbf{K_n}), it is proved that ({f SP}mathfrak{Cm}mathbf{L}={sf RCA}_n), where ({sf Cm}) is the dual operator to (sf At); that of forming complex algebras.

It is also shown that any class (mathbf{K}) between ({sf CRCA}_ncap mathbf{S_d}{sf Nr}_n{sf CA}_{omega}) and (mathbf{S_c}{sf Mushroom Gummies Nr}_n{sf CA}_{n+3}) is not first order definable, where (mathbf{S_d}) is the operation of forming dense subalgebras, and that for any (2 Report this page