The Axiom of Choice » książka
The Axiom of Choice
ISBN-13: 9781904987543 / Angielski / Miękka / 2009 / 264 str.
This book presents an overview of the development of the Axiom of Choice since its introduction by Zermelo at the beginning of the last century. The book surveys the Axiom of Choice from three perspectives. The first, or mathematical perspective, is that of the "working mathematician." This perspective brings into view the manifold applications of the Axiom of Choice-usually in the guise of Zorns Lemma- in a great variety of areas of mathematics. The second, foundational, perspective is that of the logician or constructive mathematician concerned with the foundational status of the Axiom of Choice. The third, topos-theoretical, perspective is that taken by the mathematician or logician investigating the role of the Axiom of Choice in topos theory. Certain topics-for instance mathematical applications of the Axiom, and its relationship with logic-are discussed in considerable detail. Others-notably the consistency and independence of the Axiom of the usual systems of set theory-are given no more than summary treatment, the justification here being that these topics have been given full expositions elsewhere. It is hoped that the book will be of interest to logicians and mathematicians, both professional and prospective.
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.
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