This work gives the first relativized world where the polynomial-time
hierarchy acts like the arithmetic hierarchy, i.e., for all
$k$,
$\Sigma_k^p \ne \Pi_k^p$ and $\Sigma_k^p \cap \Pi_k^p=\Delta_k^p$.
In addition our oracle makes $\P \ne \UP$ and for
every $\NP$ machine $M$ that accepts $\Sigma^*$, there is
a polynomial-time function $f$ such that $f(x)$ is an accepting
path in the computation $M(x)$.
This is also the first relativized world where the latter
condition holds and the polynomial-time hierarchy is infinite
answering an open question of Fenner, Fortnow, Naik and Rogers.
To create the oracle, we introduce Kolmogorov-generic oracles
where the strings placed in the oracle are derived from an
exponentially long Kolmogorov-random string.