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THE ARITHMETIC OF THE EVEN AND THE ODD

Published online by Cambridge University Press:  18 January 2016

VICTOR PAMBUCCIAN
VICTOR PAMBUCCIAN*
Affiliation:
School of Mathematical and Natural Sciences, Arizona State University
*
*SCHOOL OF MATHEMATICAL AND NATURAL SCIENCES ARIZONA STATE UNIVERSITY - WEST CAMPUS P. O. BOX 37100, PHOENIX, AZ 85069-7100 E-mail: [email protected]
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Abstract

We present several formal theories for the arithmetic of the even and the odd, show that the irrationality of $\sqrt 2$ can be proved in one of them, that the proof must involve contradiction, and prove that the irrationality of $\sqrt {17}$ cannot be proved inside any formal theory of the even and the odd.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 9 , Issue 2 , June 2016 , pp. 359 - 369
Copyright
Copyright © Association for Symbolic Logic 2016 

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