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FINITE RELATION ALGEBRAS

Part of: Algebraic logic Model theory

Published online by Cambridge University Press:  19 October 2021

JAMES MATHEW KOUSSAS Open the ORCID record for JAMES MATHEW KOUSSAS [Opens in a new window]
JAMES MATHEW KOUSSAS*
Affiliation:
LA TROBE UNIVERSITY MELBOURNE, VICTORIA, AUSTRALIA
*
E-mail: jameskoussas@gmail.com
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Abstract

We will show that almost all nonassociative relation algebras are symmetric and integral (in the sense that the fraction of both labelled and unlabelled structures that are symmetric and integral tends to $1$), and using a Fraïssé limit, we will establish that the classes of all atom structures of nonassociative relation algebras and relation algebras both have $0$–$1$ laws. As a consequence, we obtain improved asymptotic formulas for the numbers of these structures and broaden some known probabilistic results on relation algebras.

Keywords

relation algebrasatom structures0-1 laws

MSC classification

Primary: 03G15: Cylindric and polyadic algebras; relation algebras
Secondary: 03C13: Finite structures

Information

Type
Article
Information
The Journal of Symbolic Logic , Volume 88 , Issue 2 , June 2023 , pp. 874 - 888
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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