Notre Dame Journal of Formal Logic 36 (2):279-298 (1995)

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Abstract
Ontologically minimal truth law semantics are provided for various branches of formal logic (classical propositional logic, S5 modal propositional logic, intuitionistic propositional logic, classical elementary predicate logic, free logic, and elementary arithmetic). For all of them logical validity/truth is defined in an ontologically minimal way, that is, not via truth value assignments or interpretations. Semantical soundness and completeness are proved (in an ontologically minimal way) for a calculus of classical elementary predicate logic
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DOI 10.1305/ndjfl/1040248459
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Realism, Mathematics, and Modality.Hartry Field - 1988 - Philosophical Topics 16 (1):57-107.
Metalogic and Modality.Hartry Field - 1991 - Philosophical Studies 62 (1):1 - 22.

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