@article{ad2836a3-e2ee-3604-b575-f1db4091797d,
    issn = {00224812, 19435886},
    url = {http://www.jstor.org/stable/43864484},
    abstract = {We give model theoretic criteria for the existence of ⴺⱯ and Ɐⴺ-formulas in the ring language to define uniformly the valuation rings O of models (K, O) of an elementary theory ∑ of henselian valued fields. As one of the applications we obtain the existence of an ⴺⱯ-formula defining uniformly the valuation rings O of valued henselian fields (K.O) whose residue class field k is finite, pseudofinite, or hilbertian. We also obtain Ɐⴺ-formulas φ₂ and φ₄, such that φ₂ defines uniformly k[[t]] in k((t)) whenever k is finite or the function field of a real or complex curve, and φ₄ replaces φ₂ if k is any number field.},
    author = {Alexander Prestel},
    journal = {The Journal of Symbolic Logic},
    number = {4},
    pages = {1260--1267},
    publisher = {[Association for Symbolic Logic, Cambridge University Press]},
    title = {Definable Henselian Valuation Rings},
    urldate = {2024-10-22},
    volume = {80},
    year = {2015},
    date-added = {2024-10-22 15:14:47 +0100}
}

@article{ad2836a3-e2ee-3604-b575-f1db4091797d, issn = {00224812, 19435886}, url = {http://www.jstor.org/stable/43864484}, abstract = {We give model theoretic criteria for the existence of ⴺⱯ and Ɐⴺ-formulas in the ring language to define uniformly the valuation rings O of models (K, O) of an elementary theory ∑ of henselian valued fields. As one of the applications we obtain the existence of an ⴺⱯ-formula defining uniformly the valuation rings O of valued henselian fields (K.O) whose residue class field k is finite, pseudofinite, or hilbertian. We also obtain Ɐⴺ-formulas φ₂ and φ₄, such that φ₂ defines uniformly k[[t]] in k((t)) whenever k is finite or the function field of a real or complex curve, and φ₄ replaces φ₂ if k is any number field.}, author = {Alexander Prestel}, journal = {The Journal of Symbolic Logic}, number = {4}, pages = {1260--1267}, publisher = {[Association for Symbolic Logic, Cambridge University Press]}, title = {Definable Henselian Valuation Rings}, urldate = {2024-10-22}, volume = {80}, year = {2015}, date-added = {2024-10-22 15:14:47 +0100} }