On Crawley Modules

ABSTRACT

This continues recent work in an article by Corner et al. (2004). A particular question was left open: Is it possible to carry over the results concerning the undecidability of torsion-free Crawley groups to modules over the ring of p-adic integers? We will confirm this and also strengthen one of the results in Corner et al. (2004) by replacing the hypothesis of ⋄ by CH. For details see the introduction.

Key Words:

• Criteria for freeness
• Torsion-free modules over the p-adic integers
• Undecidability

Mathematics Subject Classification:

• 20K40
• 03E50
• 13C10

ACKNOWLEDGMENTS

This work is supported by the project No. I-706-54.6/2001 of the German-Israeli Foundation for Scientific Research & Development. The authors would also like to thank the Edmund Landau Center for partial support of this research Shelah's list of publications GbSh 833.

Notes

Communicated by K. Rangaswamy.