When are profinite many-sorted algebras retracts of ultraproducts of finite many-sorted algebras?
نویسندگان
چکیده
منابع مشابه
Many Sorted Algebras
The basic purpose of the paper is to prepare preliminaries of the theory of many sorted algebras. The concept of the signature of a many sorted algebra is introduced as well as the concept of many sorted algebra itself. Some auxiliary related notions are defined. The correspondence between (1 sorted) universal algebras [8] and many sorted algebras with one sort only is described by introducing ...
متن کاملProducts of Many Sorted Algebras
For simplicity we follow the rules: I, J denote sets, A, B denote many sorted sets of I, i, j, x are arbitrary, and S denotes a non empty many sorted signature. A set has common domain if: (Def.1) For all functions f , g such that f ∈ it and g ∈ it holds dom f = dom g. Let us mention that there exists a set which is functional and non empty and has common domain. The following proposition is tr...
متن کاملOn the Trivial Many Sorted Algebras and Many Sorted Congruences
In this paper a, I denote sets and S denotes a non empty non void many sorted signature. The scheme MSSExD deals with a non empty set A and a binary predicate P , and states that: There exists a many sorted set f indexed by A such that for every element i of A holds P [i, f (i)] provided the following condition is met: • For every element i of A there exists a set j such that P [i, j]. Let I be...
متن کاملEquations in Many Sorted Algebras
This paper is preparation to prove Birkhoff’s Theorem. Some properties of many sorted algebras are proved. The last section of this work shows that every equation valid in a many sorted algebra is also valid in each subalgebra, and each image of it. Moreover for a family of many sorted algebras (Ai : i ∈ I) if every equation is valid in each Ai, i ∈ I then is also valid in product ∏(Ai : i ∈ I).
متن کاملInverse Limits of Many Sorted Algebras
We adopt the following rules: P denotes a non empty poset, i, j, k denote elements of P , and S denotes a non void non empty many sorted signature. Let I be a non empty set, let us consider S, let A1 be an algebra family of I over S, let i be an element of I, and let o be an operation symbol of S. One can verify that (OPER(A1))(i)(o) is function-like and relation-like. Let I be a non empty set,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Logic Journal of the IGPL
سال: 2018
ISSN: 1367-0751,1368-9894
DOI: 10.1093/jigpal/jzy005