Abstract
Płonka sums consist of an algebraic construction similar, in some sense, to direct limits, which allows to represent classes of algebras defined by means of regular identities (namely those equations where the same set of variables appears on both sides). Recently, Płonka sums have been connected to logic, as they provide algebraic semantics to logics obtained by imposing a syntactic filter to given logics. In this paper, I present a very general topological duality for classes of algebras admitting a Płonka sum representation in terms of dualisable algebras.
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Acknowledgements
The work of the author is supported by the European Research Council, ERC Starting Grant GA:639276: “Philosophy of Pharmacology: Safety, Statistical Standards, and Evidence Amalgamation”. The author expresses his gratitude to Andrea Loi and Anna Romanowska for the fruitful discussions on the topics of this paper.
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Presented at Unilog’2018, Vichy, France, as the winner of the SILFS (Italian Society for Logic and the Philosophy of Science) Logic Prize 2018 and candidate for the Universal Logic Prize 2018.
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Bonzio, S. Dualities for Płonka Sums. Log. Univers. 12, 327–339 (2018). https://doi.org/10.1007/s11787-018-0209-4
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DOI: https://doi.org/10.1007/s11787-018-0209-4