Robinson’s consistency theorem in soft model theory

Mundici, Daniele

doi:10.1090/S0002-9947-1981-0590421-1

Robinson’s consistency theorem in soft model theory
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Trans. Amer. Math. Soc. 263 (1981), 231-241 Request permission

Abstract:

In a soft model-theoretical context, we investigate the properties of logics satisfying the Robinson consistency theorem; the latter is for many purposes the same as the Craig interpolation theorem together with compactness. Applications are given to H. Friedman’s third and fourth problem.

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An algebraic result about soft model theoretical equivalence relations with an application to H. Friedman’s fourth problem

Compactness + Craig interpolation = Robinson’s consistency in any logic

Daniele Mundici, Compactness = JEP in any logic, Fund. Math. 116 (1983), no. 2, 99–108. MR 716223, DOI 10.4064/fm-116-2-99-108

Compactness, interpolation and H. Friedman’s third problem