Abstract
AbstractWe extend an independence result proved in [1]. We show that for all n, there is a special set of Πn sentences {φa}a ∈ H corresponding to elements of a linear ordering (H, <H) of order type . These sentences allow us to build completions {Ta}a ∈ H of PA such that for a <H b, Ta ∩ Σn ⊂ Tb ∩ Σn, with φa ∈ Ta, ¬φa ∈ Th. Our method uses the Barwise-Kreisel Compactness Theorem.
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