Relatively Recursively Enumerable Versus Relatively Σ1 in Models of Peano Arithmetic

Grzegorz J. Michalski

doi:10.1002/malq.19950410408

Relatively Recursively Enumerable Versus Relatively Σ₁ in Models of Peano Arithmetic

Grzegorz J. Michalski

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	515-522
Number of pages	8
Journal	Mathematical Logic Quarterly
Volume	41
Issue number	4
DOIs	https://doi.org/10.1002/malq.19950410408
State	Published - 1995

Scopus Subject Areas

Logic

Keywords

Forcing
Models of Peano Arithmetic
Recursively enumerable
Σ definable

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10.1002/malq.19950410408License: Unspecified

Cite this

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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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KW - Σ definable

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