Saturated models of universal theories

Annals of Pure and Applied Logic 118 (3):219-234 (2002)
Abstract
A notion called Herbrand saturation is shown to provide the model-theoretic analogue of a proof-theoretic method, Herbrand analysis, yielding uniform model-theoretic proofs of a number of important conservation theorems. A constructive, algebraic variation of the method is described, providing yet a third approach, which is finitary but retains the semantic flavor of the model-theoretic version
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Morteza Moniri (2007). Preservation Theorems for Bounded Formulas. Archive for Mathematical Logic 46 (1):9-14.
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