Fundamental order and the number of countable models

• Main Author: Tanović, Predrag
• Other Authors: Loveys, James (advisor)
• Format: Others
• Language: en
• Published: McGill University 1994
• Subjects: Mathematics.
• Online Access: http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=28543

Let T be a complete, first order theory in a countable language. We investigate certain nonisolation properties of types in small superstable theories. Also, we prove that T has 2$ sp aleph$o nonisomorphic countable models in the following cases. (A) T is strictly stable and the order type of rationals cannot be embedded into O(T) and there is no strictly stable group interpretable in T$ rm sp{ sp.q}.$ (B) T is superstable, the generic of every simple group definable in T$ rm sp{ sp.eq}$ is orthogonal to all NENI types and rm sup {U(p) vert p{ in}S(T) } geq omega sp omega .