A simplicity theorem for amoebas over random reals
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- by Fred G. Abramson PDF
- Proc. Amer. Math. Soc. 78 (1980), 409-413 Request permission
Abstract:
Let M be a countable standard transitive model of ZFC, $\mathcal {A}$ 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 $\mathcal {A}$ with $X \in M[r];(b)\;If\;\{ {x_n}|n < \omega \} \in M[r]$ is a sequence of distinct reals, then for all large enough n, $\{ {x_i}|{2^n} \leqslant i < {2^{n + 1}}\} \cap \mathcal {A} \ne \emptyset$.References
- D. A. Martin and R. M. Solovay, Internal Cohen extensions, Ann. Math. Logic 2 (1970), no. 2, 143–178. MR 270904, DOI 10.1016/0003-4843(70)90009-4
- 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 265151, DOI 10.2307/1970696
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 78 (1980), 409-413
- MSC: Primary 03E40; Secondary 28A20
- DOI: https://doi.org/10.1090/S0002-9939-1980-0553385-7
- MathSciNet review: 553385