I'm following the Jech's Multiple Forcing for a seminar group and I intend to show how to add one or some reals to extensions.

I studied Solovay's model and I can see why learning how to add random reals is an important tool, as well as adding Cohen reals, etc.

My doubt is concerned to reals like Sacks, Pikry-Silver, Mathias, Laver and Grigorieff.

Where were these reals relevant to solve questions related to consistency results?

Thank you!