Geometry of super-Łukasiewicz logics

Nola, Antonio Di; Lenzi, Giacomo; Vitale, Gaetano

doi:10.1093/logcom/exab060

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Spectra Of Free Mv-algebras In V(c)1

A Functor From V(c)-algebras To Topological Spaces1

Note That the Inclusion Can Be Replaced With Equality1

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2023

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“…Since ∆(R) generates V(C), the free V(C)-algebra over a cardinal k can be defined as the MV-algebra of polynomial functions from ∆(R) k to ∆(R), see [17,Theorem 8.1].…”

Section: Spectra Of Free Mv-algebras In V(c)mentioning

confidence: 99%

“…this is an MV-algebra which generates V(K m ) (see [17,Theorem 2.1]). We can say that ∆ m (R) is the continuous analogue of K m .…”

Section: A Functor From V(c)-algebras To Topological Spacesmentioning

confidence: 99%

“…Proof. It follows from the description of MV-polynomials in ∆(R) F given in [17,Theorem 3.1] with m = 1.…”

Section: Note That the Inclusion Can Be Replaced With Equalitymentioning

confidence: 99%

See 2 more Smart Citations

The spectrum problem for $\ell$-groups and for MV-algebras: a categorical approach

Barbieri¹,

Nola²,

Lenzi³

2023

Preprint

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As a main result, we characterize prime spectra of abelian lattice ordered groups. Further we introduce some categories based on spectral spaces, lattices and Priestley spaces, and we relate these categories with each other and with the category of presented MV-algebras, by means of functors. We turn to lattices and offer a simple characterization of 1) maps whose Stone dual preserves closed sets, and 2) closed epimorphisms between distributive lattices as well as their Stone duals. We have a characterization of the variety generated by the Chang MV-algebra and we study this variety. Next we generalize the results to every variety generated by a Komori chain. Finally we discuss homogeneous polynomials in MV-algebras.

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“…Since ∆(R) generates V(C), the free V(C)-algebra over a cardinal k can be defined as the MV-algebra of polynomial functions from ∆(R) k to ∆(R), see [17,Theorem 8.1].…”

Section: Spectra Of Free Mv-algebras In V(c)mentioning

confidence: 99%

“…this is an MV-algebra which generates V(K m ) (see [17,Theorem 2.1]). We can say that ∆ m (R) is the continuous analogue of K m .…”

Section: A Functor From V(c)-algebras To Topological Spacesmentioning

confidence: 99%

See 1 more Smart Citation

The spectrum problem for $\ell$-groups and for MV-algebras: a categorical approach

Barbieri¹,

Nola²,

Lenzi³

2023

Preprint

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Geometry of super-Łukasiewicz logics

Abstract: In this work, we provide constructions, characterizations, geometrical dualities and a McNaughton theorem for non-archimedean MV-algebras, which are the semantics of super-Łukasiewicz logics introduced by Komori.

Cited by 1 publication

References 33 publications

The spectrum problem for $\ell$-groups and for MV-algebras: a categorical approach

The spectrum problem for $\ell$-groups and for MV-algebras: a categorical approach

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