Biró, B. and I. Sain, Peano arithmetic as axiomatization of the time frame in logics of programs and in dynamic logics, Annals of Pure and Applied Logic 63 201-225. We show that one can prove the partial correctness of more programs using Peano's axioms for the time frames of three-sorted time models than using only Presburger's axioms, that is it is useful to allow multiplication of time points at program verification and in dynamic and temporal logics. We organized the paper (...) as follows: 1. Preliminaries, 2. The main result, 3. Peano arithmetic with bounded multiplication, 4. Connections with temporal logics and dynamic logics, Acknowledgements, References. (shrink)