On the cardinal number of complete sets of Boolean operations†

†Communicated by Author.

Abstract

It is shown in the literature (using the Post—Yablonsky theorem) that a complete set of Boolean operations cannot have a cardinal number greater than four. It is the object of this paper to improve this bound and prove that a complete set can have a cardinal number of at most three or, in other words, there does not exist a complete (non–redundant) set of more than three Boolean operations. The proof given here is constructive, using the Post—Yablonsky theorem, truth tables and combinatorial set theory.

Notes

†Communicated by Author.

Additional information

Notes on contributors

E. V. KRISHNAMURTHY

On leave of absence from the Indian Statistical Institute, Calcutta, India.