The Logical Foundations of Nonstandard Analysis: With Applications to Economic Theory
暫譯: 非標準分析的邏輯基礎：及其在經濟理論中的應用

García de la Sienra, Adolfo

The Logical Foundations of Nonstandard Analysis: With Applications to Economic Theory
  • 出版商: Springer
  • 出版日期: 2026-02-07
  • 售價: $6,440
  • 貴賓價: 9.8 折 $6,311
  • 語言: 英文
  • 頁數: 254
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3032056764
  • ISBN-13: 9783032056764
  • 相關分類: 離散數學 Discrete-mathematics

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商品描述

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.

商品描述(中文翻譯)

這本書提供了非標準分析基礎的徹底且系統的介紹，並應用於經濟理論。從阿克曼的集合論開始，書中小心地轉向布爾代數、一階邏輯、超積、非標準宇宙、超實數系統、非標準分析本身（包括與經濟理論相關的拓撲學論述），最後探討非標準經濟學。關於非標準經濟學的章節包含了對里希特定理的完整討論和證明，該定理關於每個基數高達連續體的偏好結構存在效用表示。書中還包含了經濟理論的主要方法論定理的證明，主要是不動點定理，並以證明社會系統均衡的存在作結。涵蓋本體論、邏輯和集合論等主題，這本書對廣泛的科學哲學家、經濟學家和數學家都具有興趣。

作者簡介

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.

作者簡介(中文翻譯)

阿道夫·加西亞·德·拉·西恩拉·瓜哈爾多自2002年以來一直擔任韋拉克魯斯大學哲學研究所的研究員，並自1998年以來擔任該大學經濟學院的博弈論、微觀經濟學和數學經濟學教授。他於1983年至1988年期間在墨西哥城的經濟學研究與教學中心教授微觀經濟學。加西亞·德·拉·西恩拉博士在國際期刊和出版社發表了超過一百篇論文和書籍。除了由Springer（當時為Kluwer）出版的有關馬克思價值理論邏輯基礎的書籍和一本關於宗教哲學的選集外，加西亞·德·拉·西恩拉博士還在Routledge出版了《經濟學的結構主義理論》。他的主要研究領域是經濟學的邏輯、方法論和哲學。他是國際經濟方法網絡的成員。

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