Polyadic algebra

Polyadic algebras (more recently called Halmos algebras[1]) are algebraic structures introduced by Paul Halmos. They are related to first-order logic 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. ↑ 1.0 1.1 Michiel Hazewinkel (2000). Handbook of algebra. 2. Elsevier. pp. 87–89. ISBN 978-0-444-50396-1. https://books.google.com/books?id=EkIL1BYKjlgC&pg=PA87.
2. ↑ Jon Barwise (1989). Handbook of mathematical logic. Elsevier. pp. 293. ISBN 978-0-444-86388-1. https://books.google.com/books?id=b0Fvrw9tBcMC&pg=PA293.

## Further reading

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

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