A simplicity theorem for amoebas over random reals

Author:
Fred G. Abramson

Journal:
Proc. Amer. Math. Soc. **78** (1980), 409-413

MSC:
Primary 03E40; Secondary 28A20

MathSciNet review:
553385

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Abstract | References | Similar Articles | Additional Information

Abstract: Let *M* be a countable standard transitive model of ZFC, be an amoeba over *M*, and *r* be a random real over *M*.

Theorem. (a) *There is no infinite set of reals X contained in the complement of* with *is a sequence of distinct reals, then for all large enough n*, .

**[D]**D. A. Martin and R. M. Solovay,*Internal Cohen extensions*, Ann. Math. Logic**2**(1970), no. 2, 143–178. MR**0270904****[R]**Robert M. Solovay,*A model of set-theory in which every set of reals is Lebesgue measurable*, Ann. of Math. (2)**92**(1970), 1–56. MR**0265151**

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1980-0553385-7

Keywords:
Amoeba forcing,
Solovay forcing,
random reals

Article copyright:
© Copyright 1980
American Mathematical Society