For greater than 30 years, the writer has studied the model-theoretic points of the idea of valued fields and multi-valued fields. a number of the key effects incorporated during this e-book have been received via the writer while getting ready the manuscript. hence the targeted evaluation of the idea, as built within the booklet, has been formerly unavailable.
The e-book offers with the speculation of valued fields and mutli-valued fields. the speculation of Prüfer earrings is mentioned from the `geometric' standpoint. the writer indicates that via introducing the Zariski topology on households of valuation jewelry, it truly is attainable to distinguish very important subfamilies of Prüfer earrings that correspond to Boolean and close to Boolean households of valuation jewelry. additionally, algebraic and model-theoretic houses of multi-valued fields with close to Boolean households of valuation jewelry fulfilling the local-global precept are studied. it is vital that this precept is undemanding, i.e., it may be expressed within the language of predicate calculus. an important effects got within the e-book comprise a criterion for the elementarity of an embedding of a multi-valued box and a criterion for the uncomplicated equivalence for multi-valued fields from the category outlined by means of the extra typical simple stipulations (absolute unramification, maximality and virtually continuity of neighborhood straight forward properties). The ebook concludes with a short bankruptcy discussing the bibliographic references on hand at the fabric awarded, and a quick heritage of the most important advancements in the box.
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