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Saturation and $\Sigma_2$-transfer for ERNA

Christian Impens (UGent) and Sam Sanders (UGent)
(2009) Journal of Symbolic Logic. 74(3). p.901-913
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Abstract
Elementary Recursive Nonstandard Analysis, in short ERNA, is a constructive system of nonstandard analysis with a PRA consistency proof, proposed around 1995 by Patrick Suppes and Richard Sommer. It is built on a previous system by Rolando Chuaqui and Patrick Suppes, which was recently reconsidered by Michal R\"ossler and Emil Je\v{r}\'{a}bek. A $\Pi_{1} principle has already been added to ERNA and the consistency of the resulting theory proved in PRA. Here, we equip ERNA with $\Sigma_{2} and a saturation principle, while keeping the consistency proof inside PRA. We show that the extended theory allows for generalized transfer, a basic tool of nonstandard analysis, and interprets several strong theories, like \Sigma_{2}$ and \Sigma_{2}$.
Keywords
Weak Theories of Arithmetic, Nonstandard Analysis

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Please use this url to cite or link to this publication:

MLA
Impens, Christian, and Sam Sanders. “Saturation and $\Sigma_2$-transfer for ERNA.” Journal of Symbolic Logic 74.3 (2009): 901–913. Print.
APA
Impens, C., & Sanders, S. (2009). Saturation and $\Sigma_2$-transfer for ERNA. Journal of Symbolic Logic, 74(3), 901–913.
Chicago author-date
Impens, Christian, and Sam Sanders. 2009. “Saturation and $\Sigma_2$-transfer for ERNA.” Journal of Symbolic Logic 74 (3): 901–913.
Chicago author-date (all authors)
Impens, Christian, and Sam Sanders. 2009. “Saturation and $\Sigma_2$-transfer for ERNA.” Journal of Symbolic Logic 74 (3): 901–913.
Vancouver
1.
Impens C, Sanders S. Saturation and $\Sigma_2$-transfer for ERNA. Journal of Symbolic Logic. Association of Symbolic Logic; 2009;74(3):901–13.
IEEE
[1]
C. Impens and S. Sanders, “Saturation and $\Sigma_2$-transfer for ERNA,” Journal of Symbolic Logic, vol. 74, no. 3, pp. 901–913, 2009.
@article{898461,
  abstract     = {Elementary Recursive Nonstandard Analysis, in short ERNA, is
a  constructive system of nonstandard analysis with a PRA consistency proof, proposed around 1995 by
Patrick Suppes and Richard Sommer.  It is built on a previous system by Rolando Chuaqui and Patrick Suppes, which was recently reconsidered by Michal R\"ossler and Emil Je\v{r}\'{a}bek. 
A $\Pi_{1} principle has already been added to ERNA and the consistency of the resulting theory proved in PRA.  Here, we equip ERNA with $\Sigma_{2} and a saturation principle, while keeping the consistency proof inside PRA.  We show that the extended theory allows for generalized transfer, a basic tool of nonstandard analysis, and interprets several strong theories, like
\Sigma_{2}$ and \Sigma_{2}$.},
  author       = {Impens, Christian and Sanders, Sam},
  issn         = {0022-4812},
  journal      = {Journal of Symbolic Logic},
  keywords     = {Weak Theories of Arithmetic,Nonstandard Analysis},
  language     = {eng},
  number       = {3},
  pages        = {901--913},
  publisher    = {Association of Symbolic Logic},
  title        = {Saturation and $\Sigma_2$-transfer for ERNA},
  volume       = {74},
  year         = {2009},
}

Web of Science
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