We provide an alternative proof of the theorem saying that any Vašák (or, weakly countably determined) Banach space admits a full -projectional skeleton. The proof is done with the use of the method of elementary submodels and is comparably simple as the proof given by W. Kubiś (2009) in case of weakly compactly generated spaces.
The paper investigates idempotent, reductive, and distributive groupoids, and more generally -algebras of any type including the structure of such groupoids as reducts. In particular, any such algebra can be built up from algebras with a left zero groupoid operation. It is also shown that any two varieties of left -step reductive -algebras, and of right -step reductive -algebras, are independent for any positive integers and . This gives a structural description of algebras in the join of...
We continue the earlier research of [1]. In particular, we work out a class of regular interstices and show that selective types are realized in regular interstices. We also show that, contrary to the situation above definable elements, the stabilizer of an element inside M(0) whose type is selective need not be maximal.
We prove that the semialgebraic, algebraic, and algebraic nonsingular points of a definable set in o-minimal structure with analytic cell decomposition are definable. Moreover, the operation of taking semialgebraic points is idempotent and the degree of complexity of semialgebraic points is bounded.
In a previous paper, we introduced the notion of Boolean-like algebra as a generalisation of Boolean algebras to an arbitrary similarity type. In a nutshell, a double-pointed algebra with constants is Boolean-like in case for all the congruences and are complementary factor congruences of . We also introduced the weaker notion of semi-Boolean-like algebra, showing that it retained some of the strong algebraic properties characterising Boolean algebras. In this paper, we continue the investigation...
We study definable sets D of SU-rank 1 in , where ℳ is a countable homogeneous and simple structure in a language with finite relational vocabulary. Each such D can be seen as a ’canonically embedded structure’, which inherits all relations on D which are definable in , and has no other definable relations. Our results imply that if no relation symbol of the language of ℳ has arity higher than 2, then there is a close relationship between triviality of dependence and being a reduct of a binary...
Mono-unary algebras may be used to construct homomorphisms, subalgebras, and direct products of algebras of an arbitrary type.
We give some structures without quantifier elimination but in which the closure, and hence the interior and the boundary, of a quantifier free definable set is also a quantifier free definable set.