## Reports on Mathematical Logic

### No. 42

Kamila BENDOV'A

A weak essentially undecidable theory

A b s t r a c t. In this paper an axiomatic theory of multiplication and ordering is offered which is sound (true in the standard model $\bf N$ of natural numbers), is $\Sigma_1$ complete, and contains the theory $R$, hence is essentially incomplete and essentially undecidable.