Amalgamation functors and boundary properties in simple theories

John Goodrick, Byunghan Kim, Alexei Kolesnikov

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)169-207
Number of pages39
JournalIsrael Journal of Mathematics
Volume193
Issue number1
DOIs
Publication statusPublished - 2013 Jan 1

Fingerprint

Amalgamation
Functor
Groupoids
Uniqueness
Unstable
Groupoid
Automorphism Group
Existence and Uniqueness
Continue
First-order
Formulation
Context

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Goodrick, John ; Kim, Byunghan ; Kolesnikov, Alexei. / Amalgamation functors and boundary properties in simple theories. In: Israel Journal of Mathematics. 2013 ; Vol. 193, No. 1. pp. 169-207.
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Amalgamation functors and boundary properties in simple theories. / Goodrick, John; Kim, Byunghan; Kolesnikov, Alexei.

In: Israel Journal of Mathematics, Vol. 193, No. 1, 01.01.2013, p. 169-207.

Research output: Contribution to journalArticle

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