Publication: Recursive Axiomatisations from Separation Properties
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Issued Date
2021-09-03
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ISSN
00224812
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2-s2.0-85121134044
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Mahidol University
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SCOPUS
Bibliographic Citation
Journal of Symbolic Logic. Vol.86, No.3 (2021), 1228-1258
Suggested Citation
Rob Egrot Recursive Axiomatisations from Separation Properties. Journal of Symbolic Logic. Vol.86, No.3 (2021), 1228-1258. doi:10.1017/jsl.2021.19 Retrieved from: https://repository.li.mahidol.ac.th/handle/123456789/75828
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Title
Recursive Axiomatisations from Separation Properties
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Abstract
We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property. We use this to define the concept of a separation subclass. We use model theoretic techniques and games to show that separation subclasses whose axiomatisations are recursively enumerable in our second-order fragment can also be recursively axiomatised in their original first-order language. We pin down the expressive power of this formalism with respect to first-order logic, and investigate some questions relating to decidability and computational complexity. As applications of these results, by showing that certain classes can be straightforwardly defined as separation subclasses, we obtain first-order axiomatisability results for these classes. In particular we apply this technique to graph colourings and a class of partial algebras arising from separation logic.