Models of set theory with definable ordinals

A DO model (here also referred to a Paris model) is a model M of set theory all of whose ordinals are first order definable in M. Jeffrey Paris (1973) initiated the study of DO models and showed that (1) every consistent extension T of ZF has a DO model, and (2) for complete extensions T , T has a unique DO model up to isomorphism iff T proves V = OD. Here we provide a comprehensive treatment of Paris models. Our results include the following:

• Type: Journal
• Year: 2005
• Where: AML
• Authors: Ali Enayat
• Keywords: AML 2005, Do Model, Model M, Paris Models