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Existentially closed De Morgan algebras

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Abstract

We show that the theory of De Morgan algebras has a model completion and axiomatise it. Then we prove that it is \(\aleph _0\)-categorical and describe definable and algebraic closures in that theory. We also obtain similar results for Boole–De Morgan algebras.

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Acknowledgements

I am grateful to James Raftery for referring me to [7] for a discussion of existentially closed algebras from the point of view of natural dualities. I would also like to thank the referee for numerous useful remarks which helped to improve the presentation of the paper.

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  1. Vahagn Aslanyan

    Present address: School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK

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  1. Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Vahagn Aslanyan

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  1. Vahagn Aslanyan
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Correspondence to Vahagn Aslanyan.

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Presented by: J. G. Raftery.

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Aslanyan, V. Existentially closed De Morgan algebras. Algebra Univers. 81, 4 (2020). https://doi.org/10.1007/s00012-019-0633-1

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