Randomness, pseudorandomness and models of arithmetic

Pseudorandmness plays an important role in number theory, complexity theory and cryptography. Our aim is to use models of arithmetic to explain pseudorandomness by randomness. To this end we construct a set of models $\cal M$,acommonelement$\iota$ofthesemodelsandaprobabilitydistributionon$\cal M$,suchthatforeverypseudorandomsequence$s$,theprobabilitythat$s(\iota)=1$holdstrueinarandommodelfrom$\cal M$ is equal to 1/2.