Premium
The Dividing Line Methodology: Model Theory Motivating Set Theory
Author(s) -
Baldwin John T.
Publication year - 2021
Publication title -
theoria
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.34
H-Index - 16
eISSN - 1755-2567
pISSN - 0040-5825
DOI - 10.1111/theo.12297
Subject(s) - zermelo–fraenkel set theory , axiom of choice , model theory , mathematics , axiom , universal set , set theory , set (abstract data type) , line (geometry) , calculus (dental) , discrete mathematics , mathematical economics , algebra over a field , computer science , pure mathematics , geometry , programming language , medicine , dentistry
We explore Shelah's model‐theoretic dividing line methodology. In particular, we discuss how problems in model theory motivated new techniques in model theory, for example classifying theories by their potential (consistently with Zermelo–Fraenkel set theory with the axiom of choice (ZFC)) spectrum of cardinals in which there is a universal model. Two other examples are the study (with Malliaris) of the Keisler order leading to a new ZFC result on cardinal invariants and attempts to clarify the “main gap” by reducing the dependence of certain versions on (highly independent) cardinal arithmetic.