Constructing further distinct non-type-I definable degrees

Construct algebras whose spectra admit one rigid source relation while excluding another, thereby producing further distinct non-type-I definable degrees.

Background

The paper separates definable spectrum degrees using rigidity of homomorphisms from ergodic property-(T) orbit relations into nuclear targets. It emphasizes that further separations among non-type-I spectra must involve at least one nonnuclear algebra.

The open construction problem is to design algebras that selectively admit reductions from some rigid source relations but not others, yielding additional degrees beyond the nuclear and crossed-product examples.