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  1. Forcing, Downward Löwenheim-Skolem and Omitting Types Theorems, Institutionally.Daniel Găină - 2014 - Logica Universalis 8 (3-4):469-498.
    In the context of proliferation of many logical systems in the area of mathematical logic and computer science, we present a generalization of forcing in institution-independent model theory which is used to prove two abstract results: Downward Löwenheim-Skolem Theorem and Omitting Types Theorem . We instantiate these general results to many first-order logics, which are, roughly speaking, logics whose sentences can be constructed from atomic formulas by means of Boolean connectives and classical first-order quantifiers. These include first-order logic , logic (...)
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  • The Institution-Theoretic Scope of Logic Theorems.Răzvan Diaconescu, Till Mossakowski & Andrzej Tarlecki - 2014 - Logica Universalis 8 (3-4):393-406.
    In this essay we analyse and elucidate the method to establish and clarify the scope of logic theorems offered within the theory of institutions. The method presented pervades a lot of abstract model theoretic developments carried out within institution theory. The power of the proposed general method is illustrated with the examples of interpolation and definability, as they appear in the literature of institutional model theory. Both case studies illustrate a considerable extension of the original scopes of the two classical (...)
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  • Saturated models in institutions.Răzvan Diaconescu & Marius Petria - 2010 - Archive for Mathematical Logic 49 (6):693-723.
    Saturated models constitute one of the powerful methods of conventional model theory, with many applications. Here we develop a categorical abstract model theoretic approach to saturated models within the theory of institutions. The most important consequence is that the method of saturated models becomes thus available to a multitude of logical systems from logic or from computing science. In this paper we define the concept of saturated model at an abstract institution-independent level and develop the fundamental existence and uniqueness theorems. (...)
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  • Birkhoff Completeness in Institutions.Mihai Codescu & Daniel Găină - 2008 - Logica Universalis 2 (2):277-309.
    We develop an abstract proof calculus for logics whose sentences are ‘Horn sentences’ of the form: $(\forall X)H \Rightarrow c$ and prove an institutional generalization of Birkhoff completeness theorem. This result is then applied to the particular cases of Horn clauses logic, the ‘Horn fragment’ of preorder algebras, order-sorted algebras and partial algebras and their infinitary variants.
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