Independence in (unbounded) PAC fields, and imaginaries

Definition 1.1. A pseudo-algebraically closed field (PAC), is a field F such that every absolutely irreducible variety defined over F , has an F -rational point. Recall that an irreducible variety over F is defined as the zero-set of a prime ideal in a polynomial ring over F ; if this prime ideal generates a prime ideal in the polynomial ring over the algebraic closure F alg of F , then the variety is absolutely irreducible. The property of being PAC is first-order axiomatisable.

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