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- W2951585424 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." @default.
- W2951585424 created "2019-06-27" @default.
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- W2951585424 date "2011-05-13" @default.
- W2951585424 modified "2023-09-27" @default.
- W2951585424 title "Definability and Decidability in Infinite Algebraic Extensions" @default.
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