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  1.  16
    Omitting Types in Incomplete Theories.Enrique Casanovas & Rafel Farré - 1996 - Journal of Symbolic Logic 61 (1):236-245.
    We characterize omissibility of a type, or a family of types, in a countable theory in terms of non-existence of a certain tree of formulas. We extend results of L. Newelski on omitting $ non-isolated types. As a consequence we prove that omissibility of a family of $ types is equivalent to omissibility of each countable subfamily.
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  2.  20
    Weak Forms of Elimination of Imaginaries.Enrique Casanovas & Rafel Farré - 2004 - Mathematical Logic Quarterly 50 (2):126-140.
    We study the degree of elimination of imaginaries needed for the three main applications: to have canonical bases for types over models, to define strong types as types over algebraically closed sets and to have a Galois correspondence between definably closed sets B such that A ⊆ B ⊆ acl and closed subgroups of the Galois group Aut/A). We also characterize when the topology of the Galois group is the quotient topology.
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  3.  30
    A Transfer Theorem for Henselian Valued and Ordered Fields.Rafel Farré - 1993 - Journal of Symbolic Logic 58 (3):915 - 930.
    In well-known papers ([A-K1], [A-K2], and [E]) J. Ax, S. Kochen, and J. Ershov prove a transfer theorem for henselian valued fields. Here we prove an analogue for henselian valued and ordered fields. The orders for which this result apply are the usual orders and also the higher level orders introduced by E. Becker in [B1] and [B2]. With certain restrictions, two henselian valued and ordered fields are elementarily equivalent if and only if their value groups (with a little bit (...)
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  4.  20
    Some Model Theory for Almost Real Closed Fields.Françoise Delon & Rafel Farré - 1996 - Journal of Symbolic Logic 61 (4):1121-1152.
    We study the model theory of fields k carrying a henselian valuation with real closed residue field. We give a criteria for elementary equivalence and elementary inclusion of such fields involving the value group of a not necessarily definable valuation. This allows us to translate theories of such fields to theories of ordered abelian groups, and we study the properties of this translation. We also characterize the first-order definable convex subgroups of a given ordered abelian group and prove that the (...)
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