Wyniki wyszukiwania - Biblioteka Nauki

Nowa wersja platformy, zawierająca wyłącznie zasoby pełnotekstowe, jest już dostępna.
Przejdź na https://bibliotekanauki.pl

Ograniczanie wyników

Znaleziono wyników: 4

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: Hilbert algebras

Sortuj według:

Ogranicz wyniki do:

Representation and duality for Hilbert algebras

100%

Celani S. , Cabrer L. , Montangie D.

Open Mathematics

2009

tom 7

nr 3

463-478

In this paper we introduce a special kind of ordered topological spaces, called Hilbert spaces. We prove that the category of Hilbert algebras with semi-homomorphisms is dually equivalent to the category of Hilbert spaces with certain relations. We restrict this result to give a duality for the category of Hilbert algebras with homomorphisms. We apply these results to prove that the lattice of the deductive systems of a Hilbert algebra and the lattice of open subsets of its dual Hilbert space, are isomorphic. We explore how this duality is related to the duality given in [6] for finite Hilbert algebras, and with the topological duality developed in [7] for Tarski algebras.

Hilbert algebras with a necessity modal operator

88%

Celani S. A. , Montangie D.

Reports on Mathematical Logic

2014

tom Vol. 49

47--77

We introduce the variety of Hilbert algebras with a modal operator , called H-algebras. The variety of H-algebras is the algebraic counterpart of the {→;]}fragment of the intuitionitic modal logic IntK. We will study the theory of representation and we will give a topological duality for the variety of H-algebras. We are going to use these results to prove that the basic implicative modal logic IntK→ and some axiomatic extensions are canonical. We shall also to determine the simple and subdirectly irreducible algebras in some subvarieties of H-algebras.

Some properties of epimorphisms of Hilbert algebras

75%

Buşneag D. , Ghiţă M.

Open Mathematics

2010

tom 8

nr 1

41-52

This paper represents a start in the study of epimorphisms in some categories of Hilbert algebras. Even if we give a complete characterization for such epimorphisms only for implication algebras, the following results will make possible the construction of some examples of epimorphisms which are not surjective functions. Also, we will show that the study of epimorphisms of Hilbert algebras is equivalent with the study of epimorphisms of Hertz algebras.

Representation of Hilbert algebras and implicative semilattices

63%

Celani S.

Open Mathematics

2003

tom 1

nr 4

561-572

In this paper we shall give a topological representation for Hilbert algebras that extend the topological representation given by A. Diego in [4]. For implicative semilattices this representation gives a full duality. We shall also consider the representation for Boolean ring.