8 citations · 30 across the 9 of their papers we have counts for
10 papers
Baker-Beynon duality beyond semisimplicity
Luca Carai, Serafina Lapenta, Luca Spada
Combining tools from category theory, model theory, and non-standard analysis we extend Baker-Beynon dualities to the classes of all Abelian -groups and all Riesz spaces (als…
Relative ideals in homological categories, with an application to MV-algebras
Serafina Lapenta, Giuseppe Metere, Luca Spada
Let be a homological category and be a faithful conservative right adjoint. We introduce the notion of relative ideal with respect to , and we show that, un…
Infinitary logic and basically disconnected compact Hausdorff spaces
Antonio Di Nola, Serafina Lapenta, Ioana Leustean
We extend Łukasiewicz logic obtaining the infinitary logic whose models are algebras , where is a basically disconnected compact Hausdorff space. Eq…
An analysis of the logic of Riesz Spaces with strong unit
Antonio Di Nola, Serafina Lapenta, Ioana Leustean
We study Łukasiewicz logic enriched with a scalar multiplication with scalars taken in . Its algebraic models, called {\em Riesz MV-algebras}, are, up to isomorphism, unit i…
Notes on divisible MV-algebras
Serafina Lapenta, Ioana Leustean
In these notes we study the class of divisible MV-algebras inside the algebraic hierarchy of MV-algebras with product. We connect divisible MV-algebras with -vector latt…
Notes on MV-modules over integral domains
Serafina Lapenta
An MV-module is an MV-algebra endowed with a scalar multiplication with scalars in a PMV-algebra (i.e. an MV-algebra endowed with a binary "ring-like" product). We investigate the…
Towards understanding the Pierce-Birkhoff conjecture via MV-algebras
Serafina Lapenta, Ioana Leustean
Our main issue was to understand the connection between Łukasiewicz logic with product and the Pierce-Birkhoff conjecture, and to express it in a mathematical way. To do this we de…
A general view of the algebraic semantics of Łukasiewicz logic with product
Serafina Lapenta, Ioana Leustean
This paper aims at connecting the various classes that provide an algebraic semantics for three different conservative expansions of Lukasiewicz logic, using algebraic and category…
Scalar extensions for algebraic structures of Lukasiewicz logic
Serafina Lapenta, Ioana Leustean
In this paper we study the tensor product for MV-algebras, the algebraic structures of Łukasiewicz -valued logic. Our main results are: the proof that the tensor product is…
Stochastic independence for probability MV-algebras
Serafina Lapenta, Ioana Leustean
We prove that any MV-algebra has a faithful state can be embedded in an \em{f}MV-algebra of integrable functions. As consequence, we prove Hölder's inequality and Hausdorff moment…