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This book provides a thorough and systematic presentation of the foundations of Nonstandard Analysis with applications to economic theory. Starting from scratch, from Ackermann's set theory, it moves carefully to Boolean algebra, first order logic, ultraproducts, nonstandard universes, the system of hyper-real numbers, nonstandard analysis proper (including a disquisition on topology relevant for economic theory), and, finally, nonstandard economics. The chapter on nonstandard economics includes a complete discussion and proof of Richter's theorem about the existence of a utility representation for every preference structure of cardinality up to that of the continuum. It contains proofs of the main methodological theorems for economic theory, mainly fixed point theorems and concludes by proving the existence of equilibria for social systems. Covering topics such as ontology, logic, and set theory, this book is of interest to broad range of philosophers of science, economists and mathematicians.
List of contents
Dedication.- Preface.- Chapter 1. Classes and Sets.- Chapter 2. Boolean Algebras.- Chapter 3. First-Order Logic.- Chapter 4. Ultraproducts.- Chapter 5. The Ontology of Calculus.- Chapter 6. The Hyperreal Numbers.- Chapter 7. Infinitesimal Calculus.- Chapter 8. Topology.- Chapter 9. Nonstandard Mathematical Methods for Economic Theory.- Chapter 10. Nonstandard Economics.- Index.
About the author
Adolfo García de la Sienra Guajardo has been research fellow at the Philosophy Institute of the Veracruzana University since 2002, and professor of Game Theory, Microeconomics and Mathematical Economics at the Faculty of Economics of the same university since 1998. He was professor of microeconomics at the Center for Research and Teaching of Economics in Mexico City since 1983 to 1988. Dr. García de la Sienra has published more than one hundred papers and books in international journals and publishing houses. Beside a book on the logical foundations of the Marxian Theory of Value published by Springer (then Kluwer), and an anthology on the philosophy of religion, Dr. García de la Sienra has published A Structuralist Theory of Economics in Routledge. His main fields of interest is the logic, methodology and philosophy of economics. He is member of the International Network of Economic Method.
Summary
This book provides a thorough and systematic presentation of the foundations of Nonstandard Analysis with applications to economic theory. Starting from scratch, from Ackermann's set theory, it moves carefully to Boolean algebra, first order logic, ultraproducts, nonstandard universes, the system of hyper-real numbers, nonstandard analysis proper (including a disquisition on topology relevant for economic theory), and, finally, nonstandard economics. The chapter on nonstandard economics includes a complete discussion and proof of Richter's theorem about the existence of a utility representation for every preference structure of cardinality up to that of the continuum. It contains proofs of the main methodological theorems for economic theory, mainly fixed point theorems and concludes by proving the existence of equilibria for social systems. Covering topics such as ontology, logic, and set theory, this book is of interest to broad range of philosophers of science, economists and mathematicians.
