Hilbert and set theory
type: Item
instance of: scholarly article
title: Hilbert and set theory
zbMATH Open document ID: 0933.01015
DOI: 10.1023/A:1004908225146
author: Burton Dreben
author: Akihiro Kanamori
published in: Synthese
publication date: 2000-03-29T00:00:00Z
review text: The authors trace some manifestations of Hilbert's concern with set theory: dealing with the paradoxes, variant forms of the axiom of choice, proving the continuum hypothesis, and model-theoretic aspects of categoricity (where however the profound influence from Hilbert through E. H. Moore to Oswald Veblen in the early 1900s is missed on pp. 83-86). The authors have not consulted pertinent unpublished lecture courses, (at least) dating from 1904-1905, 1908, 1908-1909, 1917, 1918, 1921, 1923 and 1925. The final sections wonder somewhat off the title by describing Kurt Gödel's work on set theory in the 1930s, and an appendix on modern equivalents to Hilbert's finite basis theorem.
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 03-03
Mathematics Subject Classification ID: 03A05
zbMATH DE Number: 1322782
zbMATH Keywords: D. Hilbert
zbMATH Keywords: K. Gödel
zbMATH Keywords: axiomatic set theory
reviewed by: Ivor Grattan-Guinness
MaRDI profile type: Publication
full work available at URL: a:1004908225146
OpenAlex ID: W1588066506
description: scientific article; zbMATH DE number 1322782