$L_a(\finv)$

Journal of Symbolic Logic 44 (1):15 - 28 (1979)
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Abstract

The language $L_A(\Finv)$ is formed by adding the quantifier $\Finv x$ , "few x", to the infinitary logic L A on an admissible set A. A complete axiomatization is obtained for models whose universe is the set of ordinals of A and where $\Finv x$ is interpreted as there exist A-finitely many x. For well-behaved A, every consistent sentence has a model with an A-recursive diagram. A principal tool is forcing for $L_A(\Finv)$

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Computable categoricity for pseudo-exponential fields of size ℵ 1.Jesse Johnson - 2014 - Annals of Pure and Applied Logic 165 (7-8):1301-1317.

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