Strongly and solidly $\omega_1$-weak $p^{\omega\cdot 2+n}$-projective abelian $p$-groups

We define the classes of strongly $\omega_1$-weak $p^{\omega\cdot 2+n}$-projective, solidly $\omega_1$-weak $p^{\omega\cdot 2+n}$-projective and nicely $\omega_1$-weak $p^{\omega\cdot 2+n}$-projective abelian $p$-groups and study their crucial properties. This continues our recent investigations of this branch, published in Hacettepe J. Math. Stat. (2013) and Bull. Malaysian Math. Sci. Soc. (2014), respectively.