Non-Archimedean Utility Theory
In: Theory and Decision Library, An International Series in the Philosophy and Methodology of the Social and Behavioral Sciences 9
In: Theory and Decision Library 9
I. Preference Orderings and Utility Theory -- 1. Relational Systems -- 2. Preference Relations -- 3. Some Remarks on Utility Theory -- 4. Linear Inequalities -- II. Ordinal Utility -- 1. Some Classical Representation Theorems -- 2. Lexicographic Utility -- 3. Utility Theories with Respect to n?-Sets -- 4. Ultraproducts and Ultrapowers -- 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 -- III. On Numerical Relational Systems -- 1. First-Order Languages -- 2. Some Preliminary Considerations -- 3. Universal and Homogeneous Relational Systems -- 4. 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 -- 4. Extensive Utility -- 5. Conjoint Measurement of Utilities -- 6. On Certain 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 -- Appendix I. Ordinal and Cardinal Numbers -- Appendix II. Some Basic Facts about Filters and Ultrafilters -- Index of Names -- Index of Subjects.
