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We consider two situations which relate properties of filters with properties of the limit operators with respect to these filters. In the first one, we show that the space of sequences having limits with respect to a filter is itself and therefore, by a result of Dobrowolski and Marciszewski, such spaces are topologically indistinguishable. This answers a question of Dobrowolski and Marciszewski. In the second one, we characterize universally measurable filters which fulfill Fatou’s lemma.
A set A of natural numbers is finitely embeddable in another such set B if every finite subset of A has a rightward translate that is a subset of B. This notion of finite embeddability arose in combinatorial number theory, but in this paper we study it in its own right. We also study a related notion of finite embeddability of ultrafilters on the natural numbers. Among other results, we obtain connections between finite embeddability and the algebraic and topological structure of the Stone-Čech...
This paper is a survey of results on finite variable logics in finite model theory. It focusses on the common underlying techniques that unite many such results.
In this paper, we establish the following results:
(i) every strongly finite dilator is finitely presentable
in the category of endofunctors on the category of ordinals;
(ii) a dilator
F is strongly finite if and only if F is
finitely presentable in the category of dilators.
We formalize that the image of a semiring of sets [17] by an injective function is a semiring of sets.We offer a non-trivial example of a semiring of sets in a topological space [21]. Finally, we show that the finite product of a semiring of sets is also a semiring of sets [21] and that the finite product of a classical semiring of sets [8] is a classical semiring of sets. In this case, we use here the notation from the book of Aliprantis and Border [1].
Given an n-ary k-valued function f, gap(f) denotes the essential arity gap of f which is the minimal number of essential variables in f
which become fictive when identifying any two distinct essential variables in f.
In the present paper we study the properties of the symmetric function
with non-trivial arity gap (2 ≤ gap(f)). We prove several results concerning
decomposition of the symmetric functions with non-trivial arity gap with
its minors or subfunctions. We show that all non-empty sets of...
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