Book Review: Uncountably categorical theories
1994; American Mathematical Society; Volume: 30; Issue: 2 Linguagem: Inglês
10.1090/s0273-0979-1994-00473-2
ISSN1088-9485
Autores ResumoThis book is a translation from the Russian of Boris Zilber's Doktor Nauk dissertation.It contains a large and important chunk of Zilber's work, most of it having already appeared in various papers from the late 1970s to mid-1980s.This work has had a profound effect on the development and perspectives of modern model theory.Let me begin by mentioning two (seemingly unrelated) problems solved in this book-one in combinatorial geometry/permutation group theory, the other in first-order logic.The geometrical question requires some background.A geometry here is a set X together with a closure operation cl(-) taking subsets of X to subsets of X and with the properties: (i) cl(0) = 0 .(ii) c\({a}) = {a} for each a e X .(iii) cl(Y) = \J{cl(Y') : Y' ç Y, Y' finite} whenever Y is a subset of X. (iv) For any 7 ç X, cl(cl(r)) = cl(7).(v) If Y CX, a,beX,and b € cl(Yu{a})\cl(Y) ,then aecl(Yu{b}).
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