On the Number of Countable Models of a Countable Supersimple Theory
نویسندگان
چکیده
منابع مشابه
The number of countable models of a countable supersimple theory
In this paper, we prove the number of countable models of a countable supersimple theory is either 1 or infinite. This result is an extension of Lachlan’s theorem on a superstable theory.
متن کاملThe number of countable models
Definition 1.1 T is small if for all n < ω, |Sn(∅)| ≤ ω. Remark 1.2 If T is small, then there is a countable L0 ⊆ L such that for every φ(x) ∈ L there is some φ′(x) ∈ L0 such that in T , φ(x) ≡ φ′(x). Hence, T is a definitional extension of the countable theory T0 = T L0. Proof: See Remark 14.25 in [4]. With respect to the second assertion, consider some n-ary relation symbol R ∈ LrL0. There is...
متن کاملMorley’s number of countable models
A theory formulated in a countable predicate calculus can have at most 2א0 nonisomorphic countable models. In 1961 R. L. Vaught [9] conjected that if such a theory has uncountably many countable models, then it has exactly 2א0 countable models. This would of course follow immediately if one assumed the continuum hypothesis to be true. Almost ten years later, M. Morley [5] proved that if a count...
متن کاملCountable imaginary simple unidimensional theories are supersimple
We prove that a countable simple unidimensional theory that eliminates hyperimaginaries is supersimple. This solves a problem of Shelah in the more general context of simple theories under weak assumptions.
متن کاملOn countable RCC models
Region Connection Calculus (RCC) is the most widely studied formalism of Qualitative Spatial Reasoning. It has been known for some time that each connected regular topological space provides an RCC model. These ‘standard’ models are inevitable uncountable and regions there cannot be represented finitely. This paper, however, draws researchers’ attention to RCC models that can be constructed fro...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 1999
ISSN: 0024-6107
DOI: 10.1112/s0024610799008054