The compactness of first-order logic:from gödel to lindström

1993/01/01 by John W Dawson · 4 citations
Computer Science · Mathematics · #Computability, Logic, AI Algorithms #Advanced Topology and Set Theory #Advanced Algebra and Logic

paper · doi:10.1080/01445349308837208

openalex publication_date 1993/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

Though regarded today as one of the most important results in logic, the compactness theorem was largely ignored until nearly two decades after its discovery. This paper describes the vicissitudes of its evolution and transformation during the period 1930-1970, with special attention to the roles of Kurt Gödel, A. I. Maltsev, Leon Henkin, Abraham Robinson, and Alfred Tarski

Citations

• Über Möglichkeiten im Relativkalkül
• Ultraproducts for Algebraists
• Definability and decision problems in arithmetic
• The theory of representations for Boolean algebras
• Fragments of the propositional calculus
• The completeness of the first-order functional calculus
• On Extensions of Elementary Logic
• Completeness in the theory of types
• Die Vollständigkeit der Axiome des logischen Funktionenkalküls
• Mathematical Logic

Cited by

• Wilfrid Hodges A short history of model theory
• Compactness theorem [wikipedia]
• Löwenheim–Skolem theorem [wikipedia]
• Model theory [wikipedia]