in electrical engineering, and with Edward J. McCluskey, devised the Quine–McCluskey algorithm of reducing Boolean equations to a minimum covering sum of prime implicants. Set theory While his contributions to logic include elegant expositions and a number of technical results, it is in set theory that Quine was most innovative. He always maintained that mathematics required set theory and that set theory was quite distinct from logic. He flirted with Nelson Goodman's nominalism for a while but backed away when he failed to find a nominalist grounding of mathematics. Over the course of his career, Quine proposed three axiomatic set theories. New Foundations, NF, creates and manipulates sets using a single axiom schema for set admissibility, namely an axiom schema of stratified comprehension, whereby all individuals satisfying a stratified formula compose a set. A stratified formula is one that type theory would allow, were the ontology to include types. However, Quine's set theory does not feature types. The metamathematics of NF are curious. NF allows many "large" sets the now-canonical ZFC set theory does not allow, even sets for which the axiom of choice does not hold. Since the axiom of choice holds for all finite sets, the failure of this axiom in NF proves that NF includes infinite sets. The consistency of NF relative to other formal systems adequate for mathematics is an open question, albeit that a number of candidate proofs are current in the NF community suggesting that NF is equiconsistent with Zermelo set theory without Choice. A modification of NF, NFU, due to R. B. Jensen and admitting urelements (entities that can be members of sets but that lack elements), turns out to be consistent relative to Peano arithmetic, thus vindicating the intuition behind NF. NF and NFU are the only Quinean set theories with a following. For a derivation of foundational mathematics in NF, see Rosser (1952); The set theory of Mathematical Logic is NF augmented by the proper classes of von Neumann–Bernays–Gödel set theory, except axiomatized in a much simpler way; The set theory of Set Theory and Its Logic does away with stratification and is almost entirely derived from a single axiom schema. Quine derived the foundations of mathematics once again. This book includes the definitive exposition of Quine's theory of virtual sets and relations, and surveyed axiomatic set theory as it stood circa 1960. All three set theories admit a universal class,