The Axiom of Choice 12+

📗 This book presents an overview of the development of theAxiom of Choice since its introduction by Zermelo at thebeginning of the last century. The book surveys the Axiom ofChoice from three perspectives. The first, or mathematicalperspective, is that of the "working mathematician". Thisperspective brings into view the manifold applications of theAxiom of Choice-usually in the guise of Zorn`s Lemma- in agreat variety of areas of mathematics. The second,foundational, perspective is that of the logician orconstructive mathematician concerned with the foundationalstatus of the Axiom of Choice. The third, topos-theoretical,perspective is that taken by the mathematician or logicianinvestigating the role of the Axiom of Choice in topos theory.Certain topics-for instance mathematical applications of theAxiom, and its relationship with logic-are discussed inconsiderable detail. Others-notably the consistency andindependence of the Axiom of the usual systems of settheory-are given no more than summary treatment, thejustification here being that these topics have been given fullexpositions elsewhere.It is hoped that the book will be of interest to logicians andmathematicians, both professional and prospective.