Life in the Sacks model. (English) Zbl 0999.03044

Hrušák, Michal

Acta Univ. Carol., Math. Phys. 42, No. 2, 43-58 (2001).

Summary: This note contains results which everybody knows are true but the proofs of which are not to be found in the literature. In particular, we prove that certain cardinal invariants of the continuum are small in the Sacks model and provide a proof of a theorem of J. Baumgartner stating that \(\clubsuit\) holds in the side-by-side Sacks model.

MSC:

03E17	Cardinal characteristics of the continuum
03E40	Other aspects of forcing and Boolean-valued models

Keywords:

Sacks forcing; \(\clubsuit\)-principle; cardinal invariants of the continuum; Sacks model