Hilbert, duality, and the geometrical roots of model theory

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

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.
OriginalspracheEnglisch
Seiten (von - bis)48-86
Seitenumfang39
FachzeitschriftReview of Symbolic Logic
Jahrgang11
Ausgabenummer1
DOIs
PublikationsstatusVeröffentlicht - März 2018

ÖFOS 2012

  • 603109 Logik

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