Arithmetical independence results using higher recursion theory
Copyright policy )Arithmetical independence results using higher recursion theory
AbstractWe extend an independence result proved in [1]. We show that for alln, there is a special set of Πnsentences {φa}a ∈ Hcorresponding to elements of a linear ordering (H, <H) of order type. These sentences allow us to build completions {Ta}a ∈ Hof PA such that fora <Hb, Ta∩ Σn⊂Tb∩ Σn, withφa∈Ta, ¬φa∈Th. Our method uses the Barwise-Kreisel Compactness Theorem.
- Stanford University United States
First-order arithmetic and fragments, Models of arithmetic and set theory, Nonstandard models of arithmetic, independence, Computable structure theory, computable model theory, models of arithmetic
First-order arithmetic and fragments, Models of arithmetic and set theory, Nonstandard models of arithmetic, independence, Computable structure theory, computable model theory, models of arithmetic
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