Formalizing non-standard arguments in second-order arithmetic

Publisher： Cambridge University Press

E-ISSN： 1943-5886|75|4|1199-1210

ISSN： 0022-4812

Source： The Journal of Symbolic Logic, Vol.75, Iss.4, 2010-12, pp. : 1199-1210

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

In this paper, we introduce the systems ns-ACA0 and ns-WKL0 of non-standard second-order arithmetic in which we can formalize non-standard arguments in ACA0 and WKL0, respectively. Then, we give direct transformations from non-standard proofs in ns-ACA0 or ns-WKL0 into proofs in ACA0 or WKL0.

Related content

THE PREHISTORY OF THE SUBSYSTEMS OF SECOND-ORDER ARITHMETIC

By  

Review of Symbolic Logic, Vol. 10, Iss. 2, 2017-02 ,pp. : 357-396 (40)

Cambridge University Press

Access to resources Recommend Favorite

The pointwise ergodic theorem in subsystems of second-order arithmetic

By  

The Journal of Symbolic Logic, Vol. 72, Iss. 1, 2007-03 ,pp. : 45-66 (22)

Cambridge University Press

Access to resources Recommend Favorite

INTERPRETATIONS BETWEEN ω-LOGIC AND SECOND-ORDER ARITHMETIC

By  

The Journal of Symbolic Logic, Vol. 79, Iss. 3, 2014-08 ,pp. : 845-858 (14)

Cambridge University Press

Access to resources Recommend Favorite

The Jordan curve theorem and the Schönflies theorem in weak second-order arithmetic

By Sakamoto Nobuyuki  

Archive for Mathematical Logic, Vol. 46, Iss. 5-6, 2007-07 ,pp. : 465-480 (16)

Springer Publishing Company

Access to resources Recommend Favorite

The Baire category theorem in weak subsystems of second-order arithmetic

By  

The Journal of Symbolic Logic, Vol. 58, Iss. 2, 1993-06 ,pp. : 557-578 (22)

Cambridge University Press

Access to resources Recommend Favorite