Articles liés à Non-Archimedean Utility Theory
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Synopsis
I. Preference Orderings and Utility Theory.- 1. Relational Systems.- 2. Preference Relations.- 3. Some Remarks on Utility Theory.- 3.1. On the Formal Notion of Utility Theory.- 4. Linear Inequalities.- 4.1. Theorems of Alternatives.- 4.2. An Application.- II. Ordinal Utility.- 1. Some Classical Representation Theorems.- 2. Lexicographic Utility.- 3. Utility Theories with Respect to n?-Sets.- 4. Ultraproducts and Ultrapowers.- 4.1. Some Definitions and Properties.- 4.2. Introducing Non-Standard Models of the Reals.- 4.3. Ultrapowers of the Reals Over a Countable Index Set.- 4.4. Non-Standard Models of the Rational Numbers which are also n1-Sets.- 5. Approximating an r*-Valued Utility Function by a Real Valued Function.- 6. Non-Standard Utility Functions Always Exist.- 7. Utility Functions for Partial Orderings.- 7.1. Utility Functions in the Wider Sense.- 7.2. Utility Functions in the Narrower Sense.- III. On Numerical Relational Systems.- 1. First-Order Languages.- 2. Some Preliminary Considerations.- 3. Universal and Homogeneous Relational Systems.- 4. Saturated Relational Systems.- 4.1. Some Fundamental Results.- 4.2. Special Relational Systems.- 4.3. Some Special Results for Complete Theories.- 4.4. Ultraproducts and Saturated Relational Systems.- IV. Utility Theories for More Structured Empirical Data.- 1. Some Remarks.- 2. The Empirical Status of Axioms.- 3. Utility Theories which are Axiomatizable in an Ordinary First Order Language.- 3.1. Utility Theories which are Universally Axiomatizable.- 3.2. On Suitable Numerical Relational Systems for Utility Theories which are Axiomatizable by Finitely Many Universal Sentences.- 4. Extensive Utility.- 4.1. Hölder's Theorem.- 4.2. On the Existence of Real-Valued Utility Functions for Ordered Semigroups.- 4.3. Non-Archimedean Extensive Utility.- 4.3.1. On the Empirical Status of the Axioms of Ordered Abelean Groups and the Existence of Utility Functions.- 4.3.2. The Divisible Ordered Abelean Groups.- 4.3.3. An Application of Robinson's Model Completeness Test.- 5. Conjoint Measurement of Utilities.- 6. On Certain Mean Systems.- 6.1. Archimedean Mean Systems.- 6.2. Non-Archimedean Mean Systems.- V. On Utility Spaces, The Theory of Games and the Realization of Comparative Probability Relations.- 1. A Generalization of the Von Neumann/Morgenstern Utility Theory.- 2. Non-Standard Utilities in Game Theory.- 3. Some Aspects of the Realization of Comparative Probability Relations.- 3.1. Boolean Algebras and Fields of Sets.- 3.2. On the Realization of Some Comparative Probability Relations.- Appendix I. Ordinal and Cardinal Numbers.- Appendix II. Some Basic Facts about Filters and Ultrafilters.- Index of Names.- Index of Subjects.
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