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On Levi subgroups and the Levi decomposition for groups definable in o-minimal structures

Annalisa Conversano, Anand Pillay (2013)

Fundamenta Mathematicae

We study analogues of the notions from Lie theory of Levi subgroup and Levi decomposition, in the case of groups G definable in an o-minimal expansion of a real closed field. With a rather strong definition of ind-definable semisimple subgroup, we prove that G has a unique maximal ind-definable semisimple subgroup S, up to conjugacy, and that G = R· S where R is the solvable radical of G. We also prove that any semisimple subalgebra of the Lie algebra of G corresponds to a unique ind-definable semisimple...

On logical fiberings and automated deduction in many-valued logics using Gröbner bases.

Jochen Pfalzgraf (2004)

RACSAM

The concept of logical fiberings is briefly summarized. Based on experiences with concrete examples an algorithmic approach is developed which leads to a represention of a many-valued logic as a logical fibering. The Stone isomorphism for expressing classical logical operations by corresponding polynomials can be extended to m-valued logics. On the basis of this, a classical deduction problem can be treated symbolically as a corresponding ideal membership problem using computer algebra support with...

On many-sorted ω-categorical theories

Enrique Casanovas, Rodrigo Peláez, Martin Ziegler (2011)

Fundamenta Mathematicae

We prove that every many-sorted ω-categorical theory is completely interpretable in a one-sorted ω-categorical theory. As an application, we give a short proof of the existence of non-G-compact ω-categorical theories.

On Marczewski-Burstin representable algebras

Marek Balcerzak, Artur Bartoszewicz, Piotr Koszmider (2004)

Colloquium Mathematicae

We construct algebras of sets which are not MB-representable. The existence of such algebras was previously known under additional set-theoretic assumptions. On the other hand, we prove that every Boolean algebra is isomorphic to an MB-representable algebra of sets.

On matrix rapid filters

Winfried Just, Peter Vojtáš (1997)

Fundamenta Mathematicae

Galois-Tukey equivalence between matrix summability and absolute convergence of series is shown and an alternative characterization of rapid ultrafilters on ω is derived.

On Meager Additive and Null Additive Sets in the Cantor Space 2 ω and in ℝ

Tomasz Weiss (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

Let T be the standard Cantor-Lebesgue function that maps the Cantor space 2 ω onto the unit interval ⟨0,1⟩. We prove within ZFC that for every X ⊆ 2 ω , X is meager additive in 2 ω iff T(X) is meager additive in ⟨0,1⟩. As a consequence, we deduce that the cartesian product of meager additive sets in ℝ remains meager additive in ℝ × ℝ. In this note, we also study the relationship between null additive sets in 2 ω and ℝ.

On mean value in F -quantum spaces

Beloslav Riečan (1990)

Aplikace matematiky

The paper deals with a new mathematical model for quantum mechanics based on the fuzzy set theory [1]. The indefinite integral of observables is defined and some basic properties of the integral are examined.

On metric σ-discrete spaces

Szymon Plewik, Marta Walczyńska (2016)

Banach Center Publications

By studying dimensional types of metric scattered spaces, we consider the wider class of metric σ-discrete spaces. Applying techniques relevant to this wider class, we present new proofs of some embeddable properties of countable metric spaces in such a way that they can be generalized onto uncountable metric scattered spaces. Related topics are also explored, which gives a few new results.

On Michálek's fuzzy topological spaces

Francisco Gallego Lupiañez (2001)

Kybernetika

The aim of this paper is to study some properties of Michálek’s fuzzy topology which are quite different of the classic properties of the Chang’s topology.

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