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Abstract: We introduce the notion of a lovely pair of models of a simple theory T , generalizing Poizat's "belles paires" of models of a stable theory and the third author's "generic pairs" of models of an SU-rank 1 theory. We characterise when a saturated model of the theory T P of lovely pairs is a lovely pair (that is when the notion of a lovely pair is "axiomatizable"), finding an analogue of the non finite cover property for simple theories. We show that, under these hypotheses, T P is also... (Update)
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BibTeX entry: (Update)
@misc{ university-lovely,
author = "Itay Ben-Yaacov University",
title = "Lovely Pairs of Models",
url = "citeseer.ist.psu.edu/625826.html" }
Citations (may not include all citations):42 Annals of Pure and Applied Logic (context) - Casanovas, of et al. - 1999
18 Forking in simple unstable theories (context) - Kim - 1998
17 Classification theory (context) - Shelah - 1990
17 Annals of Pure and Applied Logic (context) - Kim, Pillay et al. - 1997
14 Simplicity and the Lascar group - Hrushovski - 1998
10 Hyperimaginaries and automorphism groups - Lascar, Pillay - 2001
7 Paires de structures stables (context) - Poizat - 1983
5 Supersimple theories - Buechler, Pillay et al. - 2001
4 Lascar strong types in some simple theories - Buechler - 1999
3 Simple theories (context) - Wagner - 1999
2 Definability in low simple theories (context) - Shami - 2000
2 Applications of the group configuration theorem in simple th.. (context) - Tomasic, Wagner - 2001
2 Generic pairs of SU-rank 1 structures (context) - Vassiliev
2 Coordinatization and canonical bases (context) - Hart, Kim et al. - 2000
1 A supersimple nonlow theory (context) - Casanovas, Kim - 1998
1 Positive model theory and compact abstract theories (context) - Ben-Yaacov - 2002
1 Local supersimplicity and related concepts (context) - Casanovas, Wagner - 2001
1 Fundamental order and forking in simple theories (context) - Lascar, Pillay - 1999
1 Forking in the category of existentially closed structures - Pillay - 2000
Documents on the same site (http://www.math.uiuc.edu/People/pillay.html): More
Hyperimaginaries and Automorphism Groups - Lascar, Pillay (2000) (Correct)
Around Stable Forking - Kim, Pillay (2000) (Correct)
The Definable Multiplicity Property and Generic Automorphisms - Kikyo, Pillay (2000) (Correct)
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