Model-theoretic constructions via amalgamation and reducts
نویسندگان
چکیده
Recall that a complete first-order theory with infinite models is strongly minimal if in any of its models, every parameter-definable subset of the model is finite or cofinite. Classical examples are theories of vector spaces and algebraically closed fields; also the degenerate example of the theory of infinite ‘pure’ sets where the only structure comes from equality. Algebraic closure in a strongly minimal structure satisfies the exchange condition, so gives rise to notions of dimension and independence (corresponding to linear dimension/ independence and transcendence degree/ algebraic independence in the two classical examples).
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