Algebraic Independence Relations in Randomizations

Uri Andrews; Isaac Goldbring; H. Jerome Keisler

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arXiv · 1703.10913

Algebraic Independence Relations in Randomizations

Uri Andrews·Isaac Goldbring·H. Jerome Keisler

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Abstract

We study the properties of algebraic independence and pointwise algebraic independence in a class of continuous theories, the randomizations $T^R$ of complete first order theories $T$. If algebraic and definable closure coincide in $T$, then algebraic independence in $T^R$ satisfies extension and has local character with the smallest possible bound, but has neither finite character nor base monotonicity. For arbitrary $T$, pointwise algebraic independence in $T^R$ satisfies extension for countable sets, has finite character, has local character with the smallest possible bound, and satisfies base monotonicity if and only if algebraic independence in $T$ does.

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BibTeX RIS

Uri Andrews, Isaac Goldbring, H. Jerome Keisler. 2017-03-31. Algebraic Independence Relations in Randomizations. https://arxiv.org/abs/1703.10913

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