Axiomatization of the forcing relation with an application to Peano Arithmetic
Axiomatizing omega and omega-op powers of words
In 1978, Courcelle asked for a complete set of axioms and rules for the equational theory of (discrete regular) words equipped with the operations of product, omega power and omega-op power. In this paper we find a simple set of equations and prove they are complete. Moreover, we show that the equational theory is decidable in polynomial time.
Axiomatizing omega and omega-op powers of words
In 1978, Courcelle asked for a complete set of axioms and rules for the equational theory of (discrete regular) words equipped with the operations of product, omega power and omega-op power. In this paper we find a simple set of equations and prove they are complete. Moreover, we show that the equational theory is decidable in polynomial time.
Axiomatizing quantum MV-algebras.
We introduce the notion of p-ideal of a QMV-algebra and we prove that the class of all p-ideals of a QMV-algebra M is in one-to-one correspondence with the class of all congruence relations of M.
Axioms which imply GCH
We propose some new set-theoretic axioms which imply the generalized continuum hypothesis, and we discuss some of their consequences.
Bad Wadge-like reducibilities on the Baire space
We consider various collections of functions from the Baire space into itself naturally arising in (effective) descriptive set theory and general topology, including computable (equivalently, recursive) functions, contraction mappings, and functions which are nonexpansive or Lipschitz with respect to suitable complete ultrametrics on (compatible with its standard topology). We analyze the degree-structures induced by such sets of functions when used as reducibility notions between subsets of...
Baire category in spaces of probability measures
Balcar's theorem on supports
In A theorem on supports in the theory of semisets [Comment. Math. Univ. Carolinae 14 (1973), no. 1, 1–6] B. Balcar showed that if is a support, being an inner model of ZFC, and with , then determines a preorder "" of such that becomes a filter on generic over . We show that if the relation is replaced by a function , then there exists an equivalence relation "" on and a partial order on such that is a complete Boolean algebra, is a generic filter and for any , .
Banach spaces and large cardinals
Banach spaces without minimal subspaces – Examples
We analyse several examples of separable Banach spaces, some of them new, and relate them to several dichotomies obtained in [11],by classifying them according to which side of the dichotomies they fall.
Banach-Mazur game played in partially ordered sets
Concepts, definitions, notions, and some facts concerning the Banach-Mazur game are customized to a more general setting of partial orderings. It is applied in the theory of Fraïssé limits and beyond, obtaining simple proofs of universality of certain objects and classes.
Banach’s Continuous Inverse Theorem and Closed Graph Theorem
In this article we formalize one of the most important theorems of linear operator theory - the Closed Graph Theorem commonly used in a standard text book such as [10] in Chapter 24.3. It states that a surjective closed linear operator between Banach spaces is bounded.
Barwise Completeness Theorems For Logics With Integrals
Base-base paracompactness and subsets of the Sorgenfrey line
A topological space is called base-base paracompact (John E. Porter) if it has an open base such that every base has a locally finite subcover . It is not known if every paracompact space is base-base paracompact. We study subspaces of the Sorgenfrey line (e.g. the irrationals, a Bernstein set) as a possible counterexample.
Bases of ZF...-models.
Basic equivalences in the alternative set theory
Basic pseudorings
The concept of a basic pseudoring is introduced. It is shown that every orthomodular lattice can be converted into a basic pseudoring by using of the term operation called Sasaki projection. It is given a mutual relationship between basic algebras and basic pseudorings. There are characterized basic pseudorings which can be converted into othomodular lattices.
Basic terms of the theory of compartmental systems
Basis problems in combinatorial set theory.
Beaucoup de modèles à peu de frais