ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

1. Logic

1991 MS Classification: 3 Ohno, Hiloshi, Japan A certain proposition unprovable in number-theoretic formal system Procedure: If a positive integer is odd, the add 1 to it. If a positive integer is even, the divide it by 2. Proposition: every positive integer is transformed into 1 by applying the above procedure finite times. This trivial proposition is unprovable in the number-theoretic formal system having ′, +, · and some oter functions. The reason will be shown. Then some related matters would also be presented.