Projects per year
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 nineteenthcentury 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 modeltheoretic 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 nonEuclidean geometries), so far, little has been said about how exactly modeltheoretic 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 language  English 

Pages (fromto)  4886 
Number of pages  39 
Journal  Review of Symbolic Logic 
Volume  11 
Issue number  1 
DOIs  
Publication status  Published  Mar 2018 
Austrian Fields of Science 2012
 603109 Logic
Keywords
 AXIOMATICS
 Hilbert
 early metatheory
 history of geometry
 history of model theory
 modern axiomatics
 phrasesHilbert
Projects
 1 Finished

Structuralism: The Roots of Mathematical Structuralism
Schiemer, G. & Kolowrat, F.
1/03/17 → 28/02/22
Project: Research funding