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A simple model for a weak system of arithmetic
Published online by Cambridge University Press: 17 April 2009
Abstract
The natural, first order version of Peano's axioms (the theory T with 0, the successor function and an induction schema) is shown to possess the following nonstandard model: the natural numbers together with a collection of ‘infinite’ elements isomorphic to the integers. In fact, a complete list of the models of this theory is obtained by showing that T is equivalent to the apparently weaker theory with the induction axiom replaced by axioms stating that there are no finite cycles under the successor function and that 0 is the only non-successor.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 11 , Issue 3 , December 1974 , pp. 321 - 323
- Copyright
- Copyright © Australian Mathematical Society 1974