Abstract
We prove that for every Scott set S there are S-saturated real closed fields and S-saturated models of Presburger arithmetic.
Highlights
Recall that S ⊆ 2ω is called a Scott set if and only if: i) S is a Turing ideal, i.e., if x, y ∈ S and z ≤T x ⊕ y, z ∈ S, where x ⊕ y is the disjoint union of x and y; ii) If T ⊆ 2
If M is a nonstandard model of Peano arithmetic and a ∈ M, let r(a) = {n ∈ ω : M |= pn|a}
Lemma 1.6 If S is a countable Scott set and T ∈ S is a completion of Peano arithmetic, there is an S-saturated model of T
Summary
Recall that S ⊆ 2ω is called a Scott set if and only if: i) S is a Turing ideal, i.e., if x, y ∈ S and z ≤T x ⊕ y, z ∈ S, where x ⊕ y is the disjoint union of x and y; ii) If T ⊆ 2
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