Polyadic Spaces and Profinite Monoids

Hyperdoctrines are an algebraization of first-order logic introduced by Lawvere in [11]. In [9], Joyal defines a polyadic space as the Stone dual of a Boolean hyperdoctrine. He also proposed to recover a polyadic space from a simpler core, its Stirling kernel. We generalize this here in order to ada...

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Bibliographic Details
Published inRelational and Algebraic Methods in Computer Science Vol. 13027; pp. 292 - 308
Main Author Marquès, Jérémie
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 2021
Springer International Publishing
SeriesLecture Notes in Computer Science
Subjects
Categorical logic
Logic on words
Profinite monoids
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Summary:Hyperdoctrines are an algebraization of first-order logic introduced by Lawvere in [11]. In [9], Joyal defines a polyadic space as the Stone dual of a Boolean hyperdoctrine. He also proposed to recover a polyadic space from a simpler core, its Stirling kernel. We generalize this here in order to adapt polyadic spaces to certain classes of first-order theories. We will see how these ideas can be applied to give a correspondence between some first-order theories with a linear order symbol and equidivisible profinite semigroup with open multiplication. The inspiration comes from the paper [6] of van Gool and Steinberg, where model theory is used to study pro-aperiodic monoids.
Bibliography:This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 670624).
ISBN:3030887006
9783030887001
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-030-88701-8_18