Three essays in the study recursive utility are presented. The first is an exposition of the extant recursive utility literature. A correspondence is drawn between the discrete time axioms for recursive utility in Koopmans (1960) and the continuous time framework in Epstein (1987b). The second essay investigates the method for endogenizing the rate of time preference given in Uzawa (1968). It is shown that when applied to non-autonomous systems, the Uzawa transformation generates errors in first order conditions. We provide a simple method for extending the Uzawa transformation to non-autonomous systems. These results are applied to two stochastic optimal control problems in the third essay. In the first problem a consumer optimally allocates consumption of a given cake whose size is unknown. With an endogenous rate of time preference, it is shown that the consumption profile may be increasing monotonic under a given set of assumptions. The second problem incorporates an endogenous rate of time preference into a stochastic optimal growth model.

In this thesis possible characterizations of the category of primitive recursive functions and the category of recursive functions are studied. Closed cartesian categories, closed under the Peano-Lawvere axiom, whlch are called pre-recursive, are considered first. Representable functlons in such a category are introduced. Every primitive recursive function is representable in a pre-recursive category. In ⍕, the free pre-recursive category generated by the empty category Φ, every morphism T → N is a natural number, and every morphism N[n] → N[m] , n ∊ N, m ∊ N, represents a recursive function. Furthermore, a morphism representing a function which is not primitive recursive is found. A recursive function whlch is not representable in ⍕ is constructed. Following the above, structures of primitive recursive category and structures of recursive category are proposed, each structure generating a category whose class of representable functions is respectively the class of primitive recursive functions and the class of recursive functlons. / Pouvons-nous caractériser la catégorie des fonctions primitives récursives, la catégorie des fonctions récursives? Considérons les catégories cartésiennes fermées, fermées sous l'axiome de Peano-Lawvere, que nous appellerons pré-récursives et précisons ce qu'est une fonction représentable dans une telle catégorie. Toute fonction primitive récursive est représentable dans une catégorie pré-récursive. Dans, la catégorie pré-récursive libre engendrée par la catégorie vide, tout morphisme T->N représente un nombre naturel et tout morphisme N[n] -> N[m], n N, m N, représente une fonction récursive. De plus, on peut trouver un morphisme qui représente une fonction qui n'est pas primitive récursive et construire une fonction récursive non représentable dans $. A la suite de ces résultats, nous présentons des structures de catégorie primitive récursive et de catégorie récursive, chaque structure engendrantune catégorie dont la classe des fonctions représentables est respectivement la class des fonctions primitives récursives et celle des fonctions récursives. fr

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Thesis (Ph. D.)--University of Wisconsin--Madison, 1957. / Typescript and manuscript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf 39).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1954. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Bibliographies: leaves 30-31, 86-88.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Vita. Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1983. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf 80).

Thesis--University of Wisconsin--Madison. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf 83).

Thesis (Ph.D.)--McGill University. / Written for the Dept. of Mathematics. Typewritten MS. Bibliography: leaves [216]-217.

The notion of recursiveness is treated in a model-theoretical way by using a particular instance of Kreisel's definition of 'invariant definability'. Naming the chosen notion 'finite describability', a number of basic definitions and properties are defined and proved. As one would expect, these properties coincide with the ones for recursion theory. The equivalences of finite describability and recursiveness bring model theory and recursion theory slightly together. / Science, Faculty of / Mathematics, Department of / Graduate