We give a survey of polynomial completeness results that
apply to expanded groups, starting with the $1$-affine completeness
of expanded groups omitting type $\textbf{2}$ proved
by Kaarli (1978), Hagemann's and Herrmann's interpolation result
for such algebras (1982), Idziak's and S{\l}omczy{\'n}ska's description of polynomially
rich algebras (2001), and the description of various types
of polynomial completeness in finite expanded groups
by Mudrinski, Kapl, and the
author (2009). We relate these results to the Compatible Function
Extension Property (Kaarli, 1983).
Sprache der Kurzfassung:
Englisch
Vortragstyp:
Hauptvortrag / Eingeladener Vortrag auf einer Tagung
Forschungs-