Relatively Recursively Enumerable Versus Relatively Σ1 in Models of Peano Arithmetic

Mathematical Logic Quarterly 41 (4):515-522 (1995)
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Abstract

We show that that every countable model of PA has a conservative extension M with a subset Y such that a certain Σ1(Y)-formula defines in M a subset which is not r. e. relative to Y.

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10.1002/malq.19950410408

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reprint Michalski, Grzegorz (2006) "Relatively Recursively Enumerable Versus Relatively Σ1 in Models of Peano Arithmetic". Mathematical Logic Quarterly 41(4):515-522

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References found in this work

Models of Peano Arithmetic.Richard Kaye - 1991 - Clarendon Press.
Models and types of Peano's arithmetic.Haim Gaifman - 1976 - Annals of Mathematical Logic 9 (3):223-306.
Finite injury and Σ1-induction.Michael Mytilinaios - 1989 - Journal of Symbolic Logic 54 (1):38 - 49.

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