A modification of Shelah’s oracle-c.c. with applications

Just, Winfried

doi:10.1090/S0002-9947-1992-1022167-7

A modification of Shelah’s oracle-c.c. with applications
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Trans. Amer. Math. Soc. 329 (1992), 325-356 Request permission

Abstract:

A method of constructing iterated forcing notions that has a scope of applications similar to Shelah’s oracle-c.c. is presented. This method yields a consistency result on homomorphisms of quotient algebras of the Boolean algebra $\mathcal {P}(\omega )$. Also, it is shown to be relatively consistent with ZFC that the Boolean algebra of Lebesgue measurable subsets of the unit interval has no projective lifting.

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