Finite embeddability property for residuated groupoids
نویسنده
چکیده
A very simple proof of the finite embeddability property for residuated distributivelattice-ordered groupoids and some related classes of algebras is presented. In particular, this gives an answer to the question posed in [3, Problem 4.2]. The presented construction allows for improvement of the upper bound on the complexity of the decision procedure for the universal theory of residuated distributive-lattice-ordered groupoids, given in [5]; for chains in the class, a tight bound can be obtained.
منابع مشابه
On the Finite Embeddability Property for Residuated Ordered Groupoids
The finite embeddability property (FEP) for integral, commutative residuated ordered monoids was established by W. J. Blok and C. J. van Alten in 2002. Using Higman’s finite basis theorem for divisibility orders we prove that the assumptions of commutativity and associativity are not required: the classes of integral residuated ordered monoids and integral residuated ordered groupoids have the ...
متن کاملResiduated Frames with Applications to Decidability
Residuated frames provide relational semantics for substructural logics and are a natural generalization of Kripke frames in intuitionistic and modal logic, and of phase spaces in linear logic. We explore the connection between Gentzen systems and residuated frames and illustrate how frames provide a uniform treatment for semantic proofs of cut-elimination, the finite model property and the fin...
متن کاملSemisimplicity, Amalgamation Property and Finite Embeddability Property of Residuated Lattices
In this thesis, we study semisimplicity, amalgamation property and finite embeddability property of residuated lattices. We prove semisimplicity and amalgamation property of residuated lattices which are of purely algebraic character, by using proof-theoretic methods and results of substructural logics. On the other hand, we show the finite model property (FMP) for various substructural logics,...
متن کاملNonassociative Lambek Calculus with Additives and Context-Free Languages
We study Nonassociative Lambek Calculus with additives ∧,∨, satisfying the distributive law (Distributive Full Nonassociative Lambek Calculus DFNL). We prove that categorial grammars based on DFNL, also enriched with assumptions, generate context-free languages. The proof uses proof-theoretic tools (interpolation) and a construction of a finite model, earlier employed in [11] in the proof of Fi...
متن کاملFiniteness Properties for Idempotent Residuated Structures
A class K of similar algebras is said to have the finite embeddability property (briefly, the FEP) if every finite subset of an algebra in K can be extended to a finite algebra in K, with preservation of all partial operations. If a finitely axiomatized variety or quasivariety of finite type has the FEP, then its universal first order theory is decidable, hence its equational and quasi-equation...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Reports on Mathematical Logic
دوره 43 شماره
صفحات -
تاریخ انتشار 2008