On Defining Irreducibility
نویسنده
چکیده
This means that for all n ≥ 2, there exists no first-order sentence Fn in the language Ln = (+,−,×,=, 0, 1, In) satisfying the following property: for any real algebraic variety V of R, if we interpret the n-ary predicate In by membership to V then R |= Fn if and only if V is irreducible. Our proof will imply that irreducibility remains undefinable even if we add the exponential function to Ln. It was inspired by Wilkie’s proof that C ∞ functions are not definable [8].
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