The Logical Foundations of Nonstandard Analysis: With Applications to Economic Theory

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Adolfo García de la Sienra

The Logical Foundations of Nonstandard Analysis

Name: The Logical Foundations of Nonstandard Analysis
Price: 273.14 AUD
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ISBN: 9783032056764

With Applications to Economic Theory

Adolfo García de la Sienra

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Hardback

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English

Springer Nature Switzerland AG
07 February 2026

Economic theory & philosophy; Mathematical logic; Philosophy of science

Series: Synthese Library

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.

By: Adolfo García de la Sienra
Imprint: Springer Nature Switzerland AG
Country of Publication: Switzerland
Dimensions: Height: 235mm, Width: 155mm,
ISBN: 9783032056764
ISBN 10: 3032056764
Series: Synthese Library
Pages: 254
Publication Date: 07 February 2026
Audience: College/higher education , Professional and scholarly , Further / Higher Education , Undergraduate
Format: Hardback
Publisher's Status: Active

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.