The Logical Foundations of Nonstandard Analysis
With Applications to Economic Theory
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Beschreibung
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.
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.
Contains a thorough presentation of the foundations of nonstandard analysis Provides evidence of the main nostandard mathematical economic tools Leads the reader from Ackermann's set theory up to nonstandard analysis and its applications in economics
Autor*in
Adolfo García de la Sienra
Themen in »The Logical Foundations of Nonstandard Analysis«
Set Theory First Order Logic Foundations of Nonstandard Analysis Methodology of Nonstandard mathematical economics Boolean Algebras Ultraproducts Ontology of Infinitesimal Calculus Nonstandard Social Systems Nonstandard Fixed Point Theorems Equilibria of Nonstandard Social Systems