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  1. Functoriality of the Schmidt construction.Juan Climent Vidal & Enric Cosme Llópez - 2023 - Logic Journal of the IGPL 31 (5):822-893.
    After proving, in a purely categorial way, that the inclusion functor $\textrm {In}_{\textbf {Alg}(\varSigma )}$ from $\textbf {Alg}(\varSigma )$, the category of many-sorted $\varSigma $-algebras, to $\textbf {PAlg}(\varSigma )$, the category of many-sorted partial $\varSigma $-algebras, has a left adjoint $\textbf {F}_{\varSigma }$, the (absolutely) free completion functor, we recall, in connection with the functor $\textbf {F}_{\varSigma }$, the generalized recursion theorem of Schmidt, which we will also call the Schmidt construction. Next, we define a category $\textbf {Cmpl}(\varSigma )$, of (...)
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  • Congruences and ideals on Peirce algebras: a heterogeneous/homogeneous point of view.Sandra Marques Pinto & M. Teresa Oliveira-Martins - 2012 - Mathematical Logic Quarterly 58 (4-5):252-262.
    For a Peirce algebra \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathcal P}$\end{document}, lattices \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathrm{Cong}\mathcal {P}$\end{document} of all heterogenous Peirce congruences and \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathrm{Ide}\mathcal {P}$\end{document} of all heterogenous Peirce ideals are presented. The notions of kernel of a Peirce congruence and the congruence induced by a Peirce ideal are introduced to describe an isomorphism between \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathrm{Cong}\mathcal {P}$\end{document} and \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathrm{Ide}\mathcal {P}$\end{document}. This isomorphism leads us to conclude that the class of the Peirce algebras is ideal determined. Opposed to Boolean modules case, each part of a Peirce ideal I = (...)
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