Notes on quasiminimality and excellence

Bulletin of Symbolic Logic 10 (3):334-366 (2004)
This paper ties together much of the model theory of the last 50 years. Shelah's attempts to generalize the Morley theorem beyond first order logic led to the notion of excellence, which is a key to the structure theory of uncountable models. The notion of Abstract Elementary Class arose naturally in attempting to prove the categoricity theorem for L ω 1 ,ω (Q). More recently, Zilber has attempted to identify canonical mathematical structures as those whose theory (in an appropriate logic) is categorical in all powers. Zilber's trichotomy conjecture for first order categorical structures was refuted by Hrushovski, by the introducion of a special kind of Abstract Elementary Class. Zilber uses a powerful and essentailly infinitary variant on these techniques to investigate complex exponentiation. This not only demonstrates the relevance of Shelah's model theoretic investigations to mainstream mathematics but produces new results and conjectures in algebraic geometry
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2178/bsl/1102022661
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 29,848
Through your library
References found in this work BETA
A New Strongly Minimal Set.Ehud Hrushovski - 1993 - Annals of Pure and Applied Logic 62 (2):147-166.
Toward Categoricity for Classes with No Maximal Models.Saharon Shelah & Andrés Villaveces - 1999 - Annals of Pure and Applied Logic 97 (1-3):1-25.
Stable Generic Structures.John T. Baldwin & Niandong Shi - 1996 - Annals of Pure and Applied Logic 79 (1):1-35.

View all 19 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
Added to PP index

Total downloads
20 ( #271,159 of 2,210,503 )

Recent downloads (6 months)
1 ( #387,753 of 2,210,503 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature