nLab
amalgamation property

Contents

Idea

A class of structures in model theory has the amalgamation property if for any three structures A,B,CA,B,C and embeddings f B:ABf_B: A\hookrightarrow B, f C:ACf_C: A\hookrightarrow C, there exist embeddings g B:BDg_B:B\hookrightarrow D and g C:CDg_C: C\hookrightarrow D such that g Bf B=g Cf Cg_B\circ f_B = g_C\circ f_C.

One of the simplest cases is when the free amalgam of structures B ACB\oplus_A C exists.

References

The amalgamation method for generating strongly minimal theories is introduced in

  • Ehud Hrushovski, A new strongly minimal set. Ann. Pure Appl. Logic,

    62(2):147–166, 1993. Stability in model theory, III (Trento, 1991).

Recent references include

  • Ehud Hrushovski, Groupoids, imaginaries and internal covers, arxiv/math.LO/0603413
  • Uri Andrews, Amalgamation constructions and recursive model theory, thesis, pdf
  • John T. Baldwin, Alexei Kolesnikov, Saharon Shelah, The amalgamation spectrum, J. Symbolic Logic 74:3 (2009) 914-928, MR2548468, doi
  • J D Brody, Model theory of graphs, thesis, pdf

Last revised on August 9, 2016 at 15:46:54. See the history of this page for a list of all contributions to it.