Polyadic algebra

Polyadic algebras (more recently called Halmos algebras) 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{{cite book|author=Michiel Hazewinkel|author-link=Michiel Hazewinkel|title=Handbook of algebra|volume=2|url=https://books.google.com/books?id=EkIL1BYKjlgC&pg=PA87|year=2000|publisher=Elsevier|isbn=978-0-444-50396-1|pages=87–89}} (when equality is part of the logic) and Lawvere's functorial semantics (a categorical approach).{{cite book|author=Jon Barwise|author-link=Jon Barwise|title=Handbook of mathematical logic|url=https://books.google.com/books?id=b0Fvrw9tBcMC&pg=PA293|year=1989|publisher=Elsevier|isbn=978-0-444-86388-1|pages=293}}