Polyadic algebra

Polyadic algebras (more recently called Halmos algebras[1]) are algebraic structures introduced by Paul Halmos. They are related to first-order logic in a way analogous to the relationship between Boolean algebras and propositional logic (see Lindenbaum–Tarski algebra).

There are other ways to relate first-order logic to algebra, including Tarski's cylindric algebras[1] (when equality is part of the logic) and Lawvere's functorial semantics (a categorical approach).[2]

References

1. Michiel Hazewinkel (2000). Handbook of algebra. 2. Elsevier. pp. 87–89. ISBN 978-0-444-50396-1.
2. Jon Barwise (1989). Handbook of mathematical logic. Elsevier. p. 293. ISBN 978-0-444-86388-1.

Further reading

• Paul Halmos, Algebraic Logic, Chelsea Publishing, New York (1962)