Decidability and the number of countable models
نویسندگان
چکیده
منابع مشابه
The 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...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1984
ISSN: 0168-0072
DOI: 10.1016/0168-0072(84)90009-5