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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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: 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}\vert n < \omega \} \in M[r]$ is a sequence of distinct reals, then for all large enough n, $ \{ {x_i}\vert{2^n} \leqslant i < {2^{n + 1}}\} \cap \mathcal{A} \ne \emptyset $.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0553385-7
PII: S 0002-9939(1980)0553385-7
Keywords: Amoeba forcing, Solovay forcing, random reals
Article copyright: © Copyright 1980 American Mathematical Society