By John T. Baldwin
Sleek version idea begun with Morley's categoricity theorem: A countable first-order idea that has a special (up to isomorphism) version in a single uncountable cardinal (i.e., is specific in cardinality) if and provided that a similar holds in all uncountable cardinals. during the last 35 years Shelah made nice strides in extending this end result to infinitary common sense, the place the fundamental instrument of compactness fails. He invented the concept of an summary undemanding classification to offer a unifying semantic account of theories in first-order, infinitary good judgment and with a few generalized quantifiers. Zilber constructed comparable concepts of infinitary version concept to review complicated exponentiation. This booklet offers the 1st unified and systematic exposition of this paintings. the numerous examples stretch from natural version thought to module conception and covers of Abelian kinds. Assuming just a first path in version concept, the publication expounds eventual categoricity effects (for periods with amalgamation) and categoricity in first-class sessions. Such an important instruments as Ehrenfeucht-Mostowski versions, Galois forms, tameness, omitting-types theorems, multi-dimensional amalgamation, atomic forms, solid units, vulnerable diamonds, and ideal sessions are built thoroughly and methodically. The (occasional) reliance on extensions of simple set idea is obviously laid out. The e-book concludes with a suite of open difficulties.
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