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- Theory of natural numbers.
- Object constant 0 (
*zero*). - Unary function constant ' (
*successor*).

- Object constant 0 (
- Axioms
- 0 is not the successor of any natural number:
**forall**`x`:`x`' != 0. - Different natural numbers have different successors:
**forall**`x`,`y`:`x`' =`y`' =>`x`=`y`. `F`holds for every number, if`F`holds for 0 and with every number also for its successor:(

`F`[`x`<- 0] /\ (**forall**`x`:`F`=>`F`[`x`<-`x`+1])) =>**forall**`x`:`F`.

- 0 is not the successor of any natural number:

Author: Wolfgang Schreiner

Last Modification: November 16, 1999