共查询到20条相似文献,搜索用时 8 毫秒
1.
Relation algebras from cylindric and polyadic algebras 总被引:1,自引:0,他引:1
2.
3.
We show that the variety of n-dimensional weakly higher order cylindric algebras, introduced in Németi [9], [8], is finitely axiomatizable when n > 2. Our result implies that in certain non-well-founded set theories the finitization problem of algebraic logic admits
a positive solution; and it shows that this variety is a good candidate for being the cylindric algebra theoretic counterpart
of Tarski’s quasi-projective relation algebras.
Supported by the Hungarian National Foundation for Scientific Research grant T73601. 相似文献
4.
5.
SC
, CA
, QA
and QEA
stand for the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasipolyadic algebras, and quasipolyadic equality algebras of dimension , respectively. Generalizing a result of Németi on cylindric algebras, we show that for K {SC, CA, QA, QEA} and ordinals < , the class Nr
K
of -dimensional neat reducts of -dimensional K algebras, though closed under taking homomorphic images and products, is not closed under forming subalgebras (i.e. is not a variety) if and only if > 1.From this it easily follows that for 1 < < , the operation of forming -neat reducts of algebras in K
does not commute with forming subalgebras, a notion to be made precise.We give a contrasting result concerning Halmos' polyadic algebras (with and without equality). For such algebras, we show that the class of infinite dimensional neat reducts forms a variety.We comment on the status of the property of neat reducts commuting with forming subalgebras for various reducts of polyadic algebras that are also expansions of cylindric-like algebras. We try to draw a borderline between reducts that have this property and reducts that do not.Following research initiated by Pigozzi, we also emphasize the strong tie that links the (apparently non-related) property of neat reducts commuting with forming subalgebras with proving amalgamation results in cylindric-like algebras of relations. We show that, like amalgamation, neat reducts commuting with forming subalgebras is another algebraic expression of definability and, accordingly, is also strongly related to the well-known metalogical properties of Craig, Beth and Robinson in the corresponding logics. 相似文献
6.
7.
An interpolation Theorem is proved for first order logic withinfinitary predicates. Our proof is algebraic via cylindricalgebras.1 相似文献
8.
We show that not all epimorphisms are surjective in certain classes of infinite dimensional cylindric algebras, Pinter's substitution
algebras and Halmos' quasipolyadic algebras with and without equality. It follows that these classes fail to have the strong
amalgamation property. This answers a question in [3] and a question of Pigozzi in his landmark paper on amalgamation [9].
The cylindric case was first proved by Judit Madarasz [7]. The proof presented herein is substantially different. By a result
of Németi, our result implies that the Beth-definability Theorem fails for certain expansions of first order logic 相似文献
9.
Miklós Ferenczi 《Studia Logica》2007,87(1):1-11
It is known that every α-dimensional quasi polyadic equality algebra (QPEA
α
) can be considered as an α-dimensional cylindric algebra satisfying the merrygo- round properties . The converse of this proposition fails to be true. It is investigated in the paper how to get algebras in QPEA from algebras
in CA. Instead of QPEA the class of the finitary polyadic equality algebras (FPEA) is investigated, this class is definitionally
equivalent to QPEA. It is shown, among others, that from every algebra in a β-dimensional algebra can be obtained in QPEA
β
where , moreover the algebra obtained is representable in a sense.
Presented by Daniele Mundici
Supported by the OTKA grants T0351192, T43242. 相似文献
10.
Tarek Sayed Ahmed 《Studia Logica》2007,85(2):139-151
SC, CA, QA and QEA denote the class of Pinter’s substitution algebras, Tarski’s cylindric algebras, Halmos’ quasi-polyadic
and quasi-polyadic equality algebras, respectively. Let . and . We show that the class of n dimensional neat reducts of algebras in K
m
is not elementary. This solves a problem in [2]. Also our result generalizes results proved in [1] and [2].
Presented by Robert Goldblatt 相似文献
11.
We present a finitary regularly algebraizable logic not finitely equivalential, for every similarity type. We associate to
each of these logics a class of algebras with an equivalence relation, with the property that in this class, the identity
is atomatically definable but not finitely atomatically definable.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
12.
13.
In this paper we introduced various classes of weakly associative relation algebras with polyadic composition operations. Among them is the class RWA of representable weakly associative relation algebras with polyadic composition operations. Algebras of this class are relativized representable relation algebras augmented with an infinite set of operations of increasing arity which are generalizations of the binary relative composition. We show that RWA is a canonical variety whose equational theory is decidable. 相似文献
14.
The complexity of the satisfiability problems of various arrow logics and cylindric modal logics is determined. As is well known, relativising these logics makes them decidable. There are several parameters that can be set in such a relativisation. We focus on the following three: the number of variables involved, the similarity type and the kind of relativised models considered. The complexity analysis shows the importance and relevance of these parameters. 相似文献
15.
16.
We give a new characterization of the class of completely representable cylindric algebras of dimension 2 #lt; n w via special neat embeddings. We prove an independence result connecting cylindric algebra to Martin's axiom. Finally we apply our results to finite-variable first order logic showing that Henkin and Orey's omitting types theorem fails for L
n, the first order logic restricted to the first n variables when 2 #lt; n#lt;w. L
n has been recently (and quite extensively) studied as a many-dimensional modal logic. 相似文献
17.
18.
19.
20.
The notion of an algebraic semantics of a deductive system was proposed in [3], and a preliminary study was begun. The focus of [3] was the definition and investigation of algebraizable deductive systems, i.e., the deductive systems that possess an equivalent algebraic semantics. The present paper explores the more general property of possessing an algebraic semantics. While a deductive system can have at most one equivalent algebraic semantics, it may have numerous different algebraic semantics. All of these give rise to an algebraic completeness theorem for the deductive system, but their algebraic properties, unlike those of equivalent algebraic semantics, need not reflect the metalogical properties of the deductive system. Many deductive systems that don't have an equivalent algebraic semantics do possess an algebraic semantics; examples of these phenomena are provided. It is shown that all extensions of a deductive system that possesses an algebraic semantics themselves possess an algebraic semantics. Necessary conditions for the existence of an algebraic semantics are given, and an example of a protoalgebraic deductive system that does not have an algebraic semantics is provided. The mono-unary deductive systems possessing an algebraic semantics are characterized. Finally, weak conditions on a deductive system are formulated that guarantee the existence of an algebraic semantics. These conditions are used to show that various classes of non-algebraizable deductive systems of modal logic, relevance logic and linear logic do possess an algebraic semantics. 相似文献