Links between physics and set theory

The mathematics used in physics is derivable from set theory. But do basic underlying constructs of set theory — individual axioms, objects such as infinite sets, and theorems — have any bearing on physical reality? Cited responses from set theorists typically give decidedly negative answers. This paper examines a large number of instances suggesting, to the contrary, that such constructs have direct roles in the accepted physical reality. After a brief précis of relevant set theoretic notions, applicable analogies, examples and research topics are explored to support this contrary conclusion, examining direct links between physics and set theory. Notably, many of these direct links occur in quantum mechanics. Potential implications are sketched for allied questions of mathematical realism, and of interrelations of physics and mathematics. A substantial number of the topics noted appear to warrant further study; it is hoped future researchers will take up these challenges.