No description available.

We investigate some properties of (geometric) fields in toposes of sheaves over Boolean spaces and establish the internal validity of a number of classical theorems from Algebraic Geometry and the theory of ordered fields. We then use our results to obtain, via sheaf representations, some know theorems about (von Neumann) regular rings as well as some new theorems for regular f-rings. By contrast with previous investigations in these last two subjects (Saracino and Weispfenning {39} and van den Dries {42}) a more natural approach, inspired by work of Macintyre {30}, Loullis {29}, Bunge-Reyes {7} and Bunge {4},{5} is employed here. In addition to sheaf theoretic methods we use a variety of logical methods from geometric logic, infinitary intuitionistic logic and model theory. We also prove some new theorems on the transfer of subobjects along certain morphisms and a "lifting theorem" taking truth from statements about global sections to their internal validity.

Thesis (Ph.D.)--McMaster University (Canada), 1991. / Source: Dissertation Abstracts International, Volume: 53-11, Section: B, page: 5753. Supervisor: G. Bruns.

Thesis (Ph. D.)--University of Washington, 1999. / Vita. Includes bibliographical references (leaves 170-171).

Thesis (doctoral)--Universidad de Santiago de Compostela, 1981. / Bibliography: p. 150-158.

No description available.

Η διπλωματική εργασία έχει στόχο την εισαγωγή δύο θεμάτων της αντιμεταθετικής άλγεβρας, τον εντοπισμό και τη θεωρία φασμάτων,ειδικά για αντιμεταθετικούς δακτύλιους.Ως αναγκαίο συμπλήρωμα παρουσιάσαμε μια εισαγωγή στη θεωρία δραγμάτων και δώσαμε μια έκταση στον δακτύλιο των συνεχών συναρτήσεων.Στο τελευταίο κεφάλαιο παρουσιάζουμε κάποιες εφαρμογές στη θεωρία φασμάτων και δραγμάτων. / This master thesis is an introduction of two subjects in the commutative algebra,the localization and the spectrum theory,especially for commutative rings.We also present an introduction to the sheaf theory and we give an extend to the rings of continous functions.In the last chapter we give some examples of spectrums and sheafs in some algebraic structures.

Thesis (Ph. D.)--University of Chicago, Department of Mathematics, June 2000. / Includes bibliographical references. Also available on the Internet.

Thesis (PhD (Mathematics))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: Classical formulations model belief revision as a deterministic process. Under certain circumstances, the process may have more than one outcome, which suggests that belief revision is non-deterministic instead. Representations exist that model belief revision in either format, and for both formats there are axiom schemes that determine whether the representation is in fact a belief revision process. Although the axiom scheme for the non-deterministic case generalises that of the deterministic case, both schemes entail that all of the beliefs held by an agent are affected by new information, which is perhaps unintuitive. Rather, one may consider that belief revision should be local, with beliefs only affected if the new information is pertinent to them. We approach the problem of belief revision from the standpoint that it is local and non-deterministic, and the purpose and contribution of this dissertation is the development of a topological framework with which to model belief revision in this manner. / AFRIKAANSE OPSOMMING: Geloofshersiening word gewoonlik as ’n deterministiese proses voorgestel. Meer as een uitkoms mag bestaan vir verskeie omstandighede, wat aandui dat die proses liewer nie-deterministies van aard is. Beide die gevalle word deur aksiomaskemas gereguleer, en die aksiomas vir die nie-deterministiese geval veralgemeen dié van die deterministiese geval. Albei aksiomaskemas stipuleer, miskien onintuïtief, dat alle gelowe van ’n agent deur die nuwe informasie geaffekteer word. ’n Beter metode is dat net daardie gelowe waarvoor die nuwe informasie toepaslik is geaffekteer word. Ons benader die probleem van geloofshersiening uit die standpunt dat dit lokaal en nie-deterministies is, en die doel en bydrae van hierdie proefskrif is dus die ontwikkeling van ’n topologiese raamwerk waarmee ons geloofshersiening op hierdie manier kan voorstel.

Univ., FB Mathematik, Habil.-Schr., 2001--Hamburg, 2001.