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arXiv · 1105.2792

Definability and Decidability in Infinite Algebraic Extensions

Alexandra Shlapentokh·Carlos Videla
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Abstract

We use a generalization of a construction by Ziegler to show that for any field $F$ and any countable collection of countable subsets $A_i \subseteq F, i \in \calI \subset \Z_{>0}$ there exist infinitely many fields $K$ of arbitrary positive transcendence degree over $F$ and of infinite algebraic degree such that each $A_i$ is first-order definable over $K$. We also use the construction to show that many infinitely axiomatizable theories of fields which are not compatible with the theory of algebraically closed fields are finitely hereditarily undecidable.

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BibTeXRIS

Alexandra Shlapentokh, Carlos Videla. 2011-05-13. Definability and Decidability in Infinite Algebraic Extensions. https://arxiv.org/abs/1105.2792

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