When are profinite many-sorted algebras retracts of ultraproducts of finite many-sorted algebras?
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When are profinite many-sorted algebras retracts of ultraproducts of finite many-sorted algebras?

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When are profinite many-sorted algebras retracts of ultraproducts of finite many-sorted algebras?

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dc.contributor.author Climent Vidal, J.
dc.contributor.author Cosme i Llópez, Enric
dc.date.accessioned 2019-03-13T15:04:38Z
dc.date.available 2019-03-13T15:04:38Z
dc.date.issued 2018
dc.identifier.uri http://hdl.handle.net/10550/69537
dc.description.abstract For a set of sorts S and an S-sorted signature Σ we prove that a profinite Σ-algebra, i.e. a projective limit of a projective system of finite Σ-algebras, is a retract of an ultraproduct of finite Σ-algebras if the family consisting of the finite Σ-algebras underlying the projective system is with constant support. In addition, we provide a categorial rendering of the above result. Specifically, after obtaining a category where the objects are the pairs formed by a nonempty upward directed preordered set and by an ultrafilter containing the filter of the final sections of it, we show that there exists a functor from the just mentioned category whose object mapping assigns to an object a natural transformation which is a retraction.
dc.language.iso eng
dc.relation.ispartof Logic Journal of the IGPL, 2018, vol. 26, num. 4, p. 381-407
dc.rights.uri info:eu-repo/semantics/openAccess
dc.source Climent Vidal, J. Cosme i Llópez, Enric 2018 When are profinite many-sorted algebras retracts of ultraproducts of finite many-sorted algebras? Logic Journal of the IGPL 26 4 381 407
dc.subject Àlgebra
dc.title When are profinite many-sorted algebras retracts of ultraproducts of finite many-sorted algebras?
dc.type info:eu-repo/semantics/article
dc.date.updated 2019-03-13T15:04:38Z
dc.identifier.doi https://doi.org/10.1093/jigpal/jzy005
dc.identifier.idgrec 130221

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