63 Years of the MacDowell-Specker Theorem
Roman Kossak

TL;DR
This paper surveys the extensive developments and open problems related to the MacDowell-Specker theorem, which concerns elementary extensions of models of Peano Arithmetic and has influenced many subsequent results.
Contribution
It provides a comprehensive overview of 63 years of research, generalizations, and open questions stemming from the original theorem.
Findings
Historical overview of the theorem's development
Summary of key generalizations and results
Identification of open problems in the area
Abstract
In September of 1959, at the conference on Infinitistic Methods in Warsaw, Ernst Specker presented a joint paper with Robert MacDowell in which the authors proved that every model of Peano Arithmetic has an elementary extension such that all new elements are larger than all elements of the model. Until now, the theorem has been a constant source of new results and generalizations, and there are still open problems related to it. This paper is a survey of all those developments.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical and Theoretical Analysis · Polynomial and algebraic computation · History and Theory of Mathematics
