×

On hyperhomogeneous and absolutely homogeneous models. (English. Russian original) Zbl 0936.03035

Sib. Math. J. 40, No. 2, 322-325 (1999); translation from Sib. Mat. Zh. 40, No. 2, 372-376 (1999).
A model is said to be hyperhomogeneous provided any isomorphism between its submodels can be extended to an automorphism. A model is called absolutely homogeneous provided it is \(\lambda\)-homogeneous for all \(\lambda\).
The author proves the existence of a theory in a finite language that possesses a unique hyperhomogeneous model. The cardinality of this model is \(2^\omega\).

MSC:

03C50 Models with special properties (saturated, rigid, etc.)
PDFBibTeX XMLCite