Switch to: References

Add citations

You must login to add citations.
  1. Finite axiomatizability in Łukasiewicz logic.Daniele Mundici - 2011 - Annals of Pure and Applied Logic 162 (12):1035-1047.
    We classify every finitely axiomatizable theory in infinite-valued propositional Łukasiewicz logic by an abstract simplicial complex equipped with a weight function . Using the Włodarczyk–Morelli solution of the weak Oda conjecture for toric varieties, we then construct a Turing computable one–one correspondence between equivalence classes of weighted abstract simplicial complexes, and equivalence classes of finitely axiomatizable theories, two theories being equivalent if their Lindenbaum algebras are isomorphic. We discuss the relationship between our classification and Markov’s undecidability theorem for PL-homeomorphism of (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • MVW-rigs and product MV-algebras.Alejandro Estrada & Yuri A. Poveda - 2018 - Journal of Applied Non-Classical Logics 29 (1):78-96.
    ABSTRACTWe introduce the variety of Many-Valued-Weak rigs. We provide an axiomatisation and establish, in this context, basic properties about ideals, homomorphisms, quotients and radicals. This new class contains the class of product MV-algebras presented by Di Nola and Dvurečenskij in 2001 and by Montagna in 2005. The main result is the compactness of the prime spectrum of this new class, endowed with the co-Zariski topology as defined by Dubuc and Poveda in 2010.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • A set-theoretic proof of the representation of MV-algebras by sheaves.Alejandro Estrada & Yuri A. Poveda - 2022 - Journal of Applied Non-Classical Logics 32 (4):317-334.
    In this paper, we provide a set-theoretic proof of the general representation theorem for MV-algebras, which was developed by Dubuc and Poveda in 2010. The theorem states that every MV-algebra is isomorphic to the MV-algebra of all global sections of its prime spectrum. We avoid using topos theory and instead rely on basic concepts from MV-algebras, topology and set theory.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
    		•
  • Categorical Equivalence Between $$\varvec{PMV}{\varvec{f}}$$ PMV f -Product Algebras and Semi-Low $$\varvec{f}{\varvec{u}}$$ f u -Rings.Lilian J. Cruz & Yuri A. Poveda - 2019 - Studia Logica 107 (6):1135-1158.
    An explicit categorical equivalence is defined between a proper subvariety of the class of \-algebras, as defined by Di Nola and Dvurečenskij, to be called \-algebras, and the category of semi-low \-rings. This categorical representation is done using the prime spectrum of the \-algebras, through the equivalence between \-algebras and \-groups established by Mundici, from the perspective of the Dubuc–Poveda approach, that extends the construction defined by Chang on chains. As a particular case, semi-low \-rings associated to Boolean algebras are (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
    		•
  • Lattice-ordered Abelian groups and perfect mv-algebras: A topos-theoretic perspective.Olivia Caramello & Anna Carla Russo - 2016 - Bulletin of Symbolic Logic 22 (2):170-214.
    We establish, generalizing Di Nola and Lettieri’s categorical equivalence, a Morita-equivalence between the theory of lattice-ordered abelian groups and that of perfect MV-algebras. Further, after observing that the two theories are not bi-interpretable in the classical sense, we identify, by considering appropriate topos-theoretic invariants on their common classifying topos, three levels of bi-interpretability holding for particular classes of formulas: irreducible formulas, geometric sentences, and imaginaries. Lastly, by investigating the classifying topos of the theory of perfect MV-algebras, we obtain various results (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • MV-algebras, infinite dimensional polyhedra, and natural dualities.Leonardo M. Cabrer & Luca Spada - 2017 - Archive for Mathematical Logic 56 (1-2):21-42.
    We connect the dual adjunction between MV-algebras and Tychonoff spaces with the general theory of natural dualities, and provide a number of applications. In doing so, we simplify the aforementioned construction by observing that there is no need of using presentations of MV-algebras in order to obtain the adjunction. We also provide a description of the dual maps that is intrinsically geometric, and thus avoids the syntactic notion of definable map. Finally, we apply these results to better explain the relation (...)
    No categories
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Algebraic geometry for mv-algebras.Lawrence P. Belluce, Antonio di Nola & Giacomo Lenzi - 2014 - Journal of Symbolic Logic 79 (4):1061-1091.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation