The Class of Neat Reducts is Not Elementary
نویسنده
چکیده
منابع مشابه
The Class of Neat Reducts Is Not Boolean Closed
Call a class of algebras K Boolean closed if whenever A ∈ K and B ∼= A in some Boolean valued extension of the universe of sets, then B ∈ K. SC, CA, QA and QEA stand for the classes of Pinter’s substitution algebras Tarski’s cylindric algebras, Halmos’ quasi-polyadic and quasi-polyadic equality algebras, respectively. Let 1 < n ≤ ω, n < m and K ∈ {SC,CA,QA,QEA}. We show that the class NrnKm of ...
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Cylindric algebras are the algebraic counterparts of First Order Logic as was explained in the monograph [1] of Henkin, Monk, and Tarski, and also in [2], [3], and [4]. A cylindric algebra is representable if it corresponds to some logical system in a strong sense, cf. Theorem 4.2 and Definition 6.2 in [2] and 1.1.13 of [1]. (see also the remark preceding Corollary 2 in the present note). It wa...
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We confirm a conjecture of Tarski on cylindric algebra. We confirm an old conjecture of Tarski on neat reducts of cylindric algebras. The significance of the notion of neat reducts in connection to the representation theory for cylindric algebras is well known. Indeed a classical result of Henkin, the so-called Neat Embedding Theorem says that the representable algebras in the sense of [1] 3.1....
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Looking at the operation of forming neat α-reducts as a functor, with α an infinite ordinal, we investigate when such a functor obtained by truncating ω dimensions, has a right adjoint. We show that the neat reduct functor for representable cylindric algebras does not have a right adjoint, while that of polyadic algebras is an equivalence. We relate this categorical result to several amalgamati...
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ورودعنوان ژورنال:
- Logic Journal of the IGPL
دوره 9 شماره
صفحات -
تاریخ انتشار 2001