The classical Poincaré weak recurrence theorem states that for any probability space (Ω,S, P ), any P -measure preserving transformation T , and any A ∈ S, almost all points of A return to A. In the present paper the Poincaré theorem is proved when the σ-algebra S is replaced by any σ-complete MV-algebra. Keywords— Measure preserving transformation, Poincaré recurrence theorem, σ-complete MV-al...

symmetric difference Milan Matoušek and Pavel Pták

The aim is to approve the Central limit theorem on MV-algebras by the new approach, presented by Riečan in [1]. We use the observable as a distribution function instead of the σ-homomorphism. The main idea is in local representation of σ-algebras. The following theorem is proved: Let M be a σ-complete MV-algebra with product, m : M −→ 〈0, 1〉 be a σadditive state, (xn)n be a sequence of independ...

The transport of L-sets along an L-relation R is considered, with L any residuated lattice, sometimes with further properties as to be a frame or an MV-algebra. Pairs of powerset operators related to R are considered and their basic properties are studied in a comprehensive discussion including some results already known. A few examples and suggestions for application and further development ar...

The aim of this work is to study a class of non-archimedean valued measures on MV-algebras. We call them hyperreal states and their definition naturally arise from (the uniform version of) Di Nola representation theorem for MV-algebras (cf [5, 6]): for any MV-algebra A = (A,⊕,¬,>,⊥) there exists a ultrafilter U on the cardinality of A such that A embeds into (∗[0, 1]U) Spec(A) (where as usual S...

We connect Lukasiewicz logic, a well-established many-valued logic, with weighted logics, recently introduced by Droste and Gastin. We use this connection to show that for formal series with coefficients in semirings derived from MValgebras, recognizability and definability in a fragment of second order Lukasiewicz logic coincide.

Hoop residuation algebras are the {→, 1}-subreducts of hoops; they include Hilbert algebras and the {→, 1}-reducts of MV-algebras (also known as Wajsberg algebras). The paper investigates the structure and cardinality of finitely generated algebras in varieties of kpotent hoop residuation algebras. The assumption of k-potency guarantees local finiteness of the varieties considered. It is shown ...

we consider properties of residuated lattices with universal quantifier and show that, for a residuated lattice $x$, $(x, forall)$ is a residuated lattice with a quantifier if and only if there is an $m$-relatively complete substructure of $x$. we also show that, for a strong residuated lattice $x$, $bigcap {p_{lambda} ,|,p_{lambda} {rm is an} m{rm -filter} } = {1}$ and hence that any strong re...

In [16], by using an MV-semiring and MV-algebra, we introduced the new definition of MV-semimodule studied some their basic properties. this paper, study present definitions primary ideals MV-semirings, decomposition in A-ideals MV -semimodules, MV-semimodules. Then conditions that A-ideal can have a reduced decomposition.