Hilbert, duality, and the geometrical roots of model theory

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Abstract

The article investigates one of the key contributions to modern structural mathematics, namely Hilbert’s Foundations of Geometry (1899) and its mathematical roots in nineteenth-century projective geometry. A central innovation of Hilbert’s book was to provide semantically minded independence proofs for various fragments of Euclidean geometry, thereby contributing to the development of the model-theoretic point of view in logical theory. Though it is generally acknowledged that the development of model theory is intimately bound up with innovations in 19th century geometry (in particular, the development of non-Euclidean geometries), so far, little has been said about how exactly model-theoretic concepts grew out of methodological investigations within projective geometry. This article is supposed to fill this lacuna and investigates this geometrical prehistory of modern model theory, eventually leading up to Hilbert’s Foundations.
Original languageEnglish
Pages (from-to)48-86
Number of pages39
JournalReview of Symbolic Logic
Volume11
Issue number1
DOIs
Publication statusPublished - Mar 2018

Austrian Fields of Science 2012

  • 603109 Logic

Keywords

  • AXIOMATICS
  • Hilbert
  • early metatheory
  • history of geometry
  • history of model theory
  • modern axiomatics
  • phrasesHilbert

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