Robbins Algebra

Abstract

It is shown that the Robbins problem can be fruitfully investigated by using a simplified notation for formal algebras. In this notation a nonstandard model for Robbins algebra in terms of the language itself is conjectured. The results show that any algebra satisfying the Robbins axioms is very close to being Boolean. Finiteness, or an instance of absorption (a+b=a), or an instance of idempotency (a+a=a) will push A into being Boolean. The construction of the proposed non-Boolean model for Robbins algebra is given. Also detailed are the different notations available for this model.<>