naa a22 4500 510782388 CHVBK 20180411083251.0 cr unu---uuuuu 180411e20130101xx s 000 0 eng 10.1007/s11856-012-0087-z doi (NATIONALLICENCE)springer-10.1007/s11856-012-0087-z Amalgamation functors and boundary properties in simple theories [Elektronische Daten] [John Goodrick, Byunghan Kim, Alexei Kolesnikov] This paper continues the study of generalized amalgamation properties begun in [1], [2], [3], [5] and [6]. Part of the paper provides a finer analysis of the groupoids that arise from failure of 3-uniqueness in a stable theory. We show that such groupoids must be abelian and we link the binding group of the groupoids to a certain automorphism group of the monster model, showing that the group must be abelian as well. We also study connections between n-existence and n-uniqueness properties for various "dimensions” n in the wider context of simple theories. We introduce a family of weaker existence and uniqueness properties. Many of these properties did appear in the literature before; we give a category-theoretic formulation and study them systematically. Finally, we give examples of first-order simple unstable theories showing, in particular, that there is no straightforward generalization of the groupoid construction in an unstable context. Hebrew University Magnes Press, 2012 Goodrick John Department of Mathematics, Universidad de los Andes Bogotá, Bogotá, Colombia aut Kim Byunghan Department of Mathematics, Yonsei University, 134 Shinchon-dong, Seodaemun-gu, 120-749, Seoul, South Korea aut Kolesnikov Alexei Department of Mathematics, Towson University, 8000 York Road, 21252, Towson, MD, USA aut Israel Journal of Mathematics The Hebrew University Magnes Press 193/1(2013-01-01), 169-207 0021-2172 193:1<169 2013 193 11856 https://doi.org/10.1007/s11856-012-0087-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0087-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Goodrick John Department of Mathematics, Universidad de los Andes Bogotá, Bogotá, Colombia aut NATIONALLICENCE 700 1- Kim Byunghan Department of Mathematics, Yonsei University, 134 Shinchon-dong, Seodaemun-gu, 120-749, Seoul, South Korea aut NATIONALLICENCE 700 1- Kolesnikov Alexei Department of Mathematics, Towson University, 8000 York Road, 21252, Towson, MD, USA aut NATIONALLICENCE 773 0- Israel Journal of Mathematics The Hebrew University Magnes Press 193/1(2013-01-01), 169-207 0021-2172 193:1<169 2013 193 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer