On the Completeness Interpretation of Representation Theorems

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dc.coverageSTUDIA UBB. PHILOSOPHIA, Vol. 70 (2025), 3, pp. 135-145en-US
dc.creatorLUDUŞAN, Adrian
dc.date2025-12-30
dc.date.accessioned2026-02-21T10:40:51Z
dc.descriptionRepresentation theorems, similar to their counterparts, categoricity theorems, establish an isomorphism between certain algebraic systems. However, in contrast to categoricity theorems, they have received considerably less attention in the philosophy of mathematics. The paper attempts to rectify this shortcoming by excavating the philosophical potential of representation theorems through an analysis of one of their most popular interpretations in the mathematical literature, the completeness interpretation. The meaning of this notion of completeness and the mechanism through which representation theorems are supposed to achieve it are still unclear. The paper addresses both issues. First, it proposes a definition of completeness that best suits the informal notion used in the mathematical interpretation of the theorems. Second, it formally details the mechanism responsible for achieving it. In the process, I’ll issue some remarks on the significance and relevance of the formal reconstruction of the completeness interpretation for non-eliminative structuralism. For exegetical as well as evidential reasons, I’ll focus on Cayley’s representation theorem and use it as a case study.en-US
dc.formatapplication/pdf
dc.identifierhttps://studia.reviste.ubbcluj.ro/index.php/subbphilosophia/article/view/9932
dc.identifier10.24193/subbphil.2025.3.07
dc.identifier.urihttps://hdl.handle.net/20.500.14637/1319
dc.languageeng
dc.publisherBabeș-Bolyai University / Cluj University Pressen-US
dc.relationhttps://studia.reviste.ubbcluj.ro/index.php/subbphilosophia/article/view/9932/9578
dc.rightsCopyright (c) 2025 Studia Universitatis Babeș-Bolyai Philosophiaen-US
dc.rightshttps://creativecommons.org/licenses/by-nc-nd/4.0en-US
dc.sourceStudia Universitatis Babeș-Bolyai Philosophia; Volume 70, No. 3, December 2025; 135-145en-US
dc.source2065-9407
dc.source10.24193/subbphil.2025.3
dc.subjectCayleys representation theoremen-US
dc.subjectsemantic completenessen-US
dc.subjectcategoricityen-US
dc.subjectaxiomatic completenessen-US
dc.subjectrepresentation theoremsen-US
dc.titleOn the Completeness Interpretation of Representation Theoremsen-US
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion
dc.typePeer-reviewed Articleen-US
dc.typetexten-US

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