Journal of Philosophical Logic:1-32 (forthcoming)

Authors
Guillermo Badia
University of Queensland
Patrick Girard
University of Auckland
Abstract
This paper is a step toward showing what is achievable using non-classical metatheory—particularly, a substructural paraconsistent framework. What standard results, or analogues thereof, from the classical metatheory of first order logic can be obtained? We reconstruct some of the originals proofs for Completeness, Löwenheim-Skolem and Compactness theorems in the context of a substructural logic with the naive comprehension schema. The main result is that paraconsistent metatheory can ‘re-capture’ versions of standard theorems, given suitable restrictions and background assumptions; but the shift to non-classical logic may recast the meanings of these apparently ‘absolute’ theorems.
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DOI 10.1007/s10992-022-09651-x
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References found in this work BETA

Introduction to Metamathematics.Stephen Kleene - 1952 - Princeton, NJ, USA: North Holland.
Spandrels of Truth.J. C. Beall - 2009 - Oxford, England: Oxford University Press.
Introduction to Mathematical Logic.Alonzo Church - 1944 - London: Oxford University PRess.
The Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.

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