Atomic models higher up

There exists a countable structure M of Scott rank CK 1 where M 1 = CK 1 and where the LCK 1 ,-theory of M is not -categorical. The Scott rank of a model is the least ordinal where the model is prime in its L,-theory. Most well-known models with unbounded atoms below CK 1 also realize a non-principal LCK 1 ,-type; such a model that preserves the 1-admissibility of CK 1 will have Scott rank CK

• Type: Journal
• Year: 2008
• Where: APAL
• Authors: Jessica Millar, Gerald E. Sacks
• Keywords: APAL 2008, Countable Structure, Model, Scott Rank