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Preprint Number 361
361. Vincenzo Mantova Involution on Zilber fields E-mail: Submission date: 20 September 2011. Abstract: After recalling the definition of Zilber field, and the main conjecture
behind them, we prove that Zilber fields of cardinality up to the continuum
have involutions, i.e., automorphisms of order two analogous to complex
conjugation on The proof is obtained with an explicit construction of a Zilber field with the required properties. As further applications of this technique, we also classify the exponential subfields of Zilber fields, and we produce some exponential fields with involutions such that the exponential function is order-preserving, or even continuous, and all of the axioms of Zilber fields are satisfied except for the strong exponential-algebraic closure, which is replaced by some weaker axioms. Mathematics Subject Classification: 03C60 (Primary), 08C10, 12L12 Keywords and phrases: conjugation; involution; pseudoexponentiation; real closed fields; Zilber fields |

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