Deenability of Group Theoretic Notions
نویسندگان
چکیده
We consider logical deenability of the group-theoretic notions of simplicity, nilpotency and solvability on the class of nite groups. On one hand, we show that these notions are deenable by sentences of deterministic transitive closure logic DTC. These results are based on known group-theoretic results. On the other hand, we prove that simplicity, nilpotency and the normal closure of a subset of a group are not deenable by single sentences of rst order logic FO. In addition, we show that an isomorphism between two arbitrary nite abelian groups can be expressed by a sentence of DTC(I), where DTC(I) is DTC enhanced with the equicardinality quantiier I, and that it is not expressible by a sentence of L ! 1! .
منابع مشابه
UCF Technical Report : CS - TR - 98 - 01 A Descriptive Characterization of Tree - Adjoining Languages
Since the early Sixties and Seventies it has been known that the regular and context-free languages are characterized by deenability in the monadic second-order theory of certain structures. More recently, these descriptive characterizations have been used to obtain complexity results for constraint-and principle-based theories of syntax and to provide a uniform model-theoretic framework for ex...
متن کاملA Characterization of lambda Definability in Categorical Models of Implicit Polymorphism
Lambda deenability is characterized in categorical models of simply typed lambda calculus with type variables. A category-theoretic framework known as glueing or sconing is used to extend the Jung-Tiuryn characterization of lambda deenability JuT93], rst to ccc models, and then to categorical models of the calculus with type variables. Logical relations are now a well-established tool for study...
متن کاملHereditarily Sequential Functionals
In order to deene models of simply typed functional programming languages being closer to the operational semantics of these languages, the notions of sequentiality, stability and seriality were introduced. These works originated from the deenability problem for PCF, posed in Sco72], and the full abstraction problem for PCF, raised in Plo77]. The presented computation model, forming the class o...
متن کاملThe Effect of Grammar vs. Vocabulary Pre-teaching on EFL Learners’ Reading Comprehension: A Schema-Theoretic View of Reading
This study was designed to investigate the effect of grammar and vocabulary pre-teaching, as two types of pre-reading activities, on the Iranian EFL learners’ reading comprehension from a schema–theoretic perspective. The sample consisted of 90 female students studying at pre-university centers of Isfahan. The subjects were randomly divided into three equal-in-number groups. They participated ...
متن کاملOn proof- and model-based techniques for reasoning with uncertainty
In this paper we compare two well-known techniques for reasoning with uncertainty {namely, Incidence Calculus and the Theory of Evidence { from a viewpoint not so frequently explored for such techniques. We argue that, despite the equivalence relations that these techniques have been proved to hold, they have intrinsically diierent r^ oles as representations of uncertainty for automated reasoni...
متن کامل