Categoricity, External and Internal: An Excerpt from a Conversation with Saharon Shelah

Theoria 87 (4):1001-1012 (2021)
  Copy   BIBTEX

Abstract

A long series of conversations interweaving mathematical, historical and philosophical aspects of categoricity in model theory took place between the author and Saharon Shelah in 2016 and 2017. In this excerpt of that long conversation, we explore the relationship between explicit and implicit aspects of categoricity. We also discuss the connection with definability issues.

Categories

Add categories

Keywords

Reprint years

DOI

10.1111/theo.12262

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,219

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Categoricity in abstract elementary classes with no maximal models.Monica VanDieren - 2006 - Annals of Pure and Applied Logic 141 (1):108-147.
Erratum to “Categoricity in abstract elementary classes with no maximal models” [Ann. Pure Appl. Logic 141 (2006) 108–147].Monica M. VanDieren - 2013 - Annals of Pure and Applied Logic 164 (2):131-133.
The Hart-Shelah example, in stronger logics.Saharon Shelah & Andrés Villaveces - 2021 - Annals of Pure and Applied Logic 172 (6):102958.
Categoricity of Uncountable Theories.Saharon Shelah & Leon Henkin - 1981 - Journal of Symbolic Logic 46 (4):866-867.
Review: Saharon Shelah, Leon Henkin, Categoricity of Uncountable Theories. [REVIEW]Daniel Lascar - 1981 - Journal of Symbolic Logic 46 (4):866-867.
Saharon Shelah. Infinite abelian groups, Whitehead problem and some constructions. Israel journal of mathematics, vol. 18 , pp. 243–256. - Saharon Shelah. A compactness theorem for singular cardinals, free algebras, Whitehead problem and transversals. Israel journal of mathematics, vol. 21 , pp. 319–349. - Sharaon Shelah. Whitehead groups may be not free, even assuming CH, I. Israel journal of mathematics, vol. 28 , pp. 193–204. - Saharon Shelah. Whitehead groups may not be free even assuming CH, II. Israel journal of mathematics, vol. 35 , pp. 257–285. - Saharon Shelah. On uncountable abelian groups. Israel journal of mathematics, vol. 32 , pp. 311–330. - Shai Ben-David. On Shelah's compactness of cardinals. Israel journal of mathematics, vol. 31 , pp. 34–56 and p. 394. - Howard L. Hiller and Saharon Shelah. Singular cohomology in L. Israel journal of mathematics, vol. 26 , pp. 313–319. - Howard L. Hiller, Martin Huber, and Saharon Shelah. The structure of Ext and V = L. Mathematische. [REVIEW]Ulrich Felgner - 1986 - Journal of Symbolic Logic 51 (4):1068-1070.
Maryanthe Malliaris and Saharon Shelah, Cofinality spectrum problems in model theory, set theory and general topology. Journal of the American Mathematical Society, vol. 29 , pp. 237–297. - Maryanthe Malliaris and Saharon Shelah, Existence of optimal ultrafilters and the fundamental complexity of simple theories. Advances in Mathematics, vol. 290 , pp. 614–681. - Maryanthe Malliaris and Saharon Shelah, Keisler’s order has infinitely many classes. Israel Journal of Mathematics, to appear, https://math.uchicago.edu/∼mem/. [REVIEW]H. Jerome Keisler - 2017 - Bulletin of Symbolic Logic 23 (1):117-121.
Toward categoricity for classes with no maximal models.Saharon Shelah & Andrés Villaveces - 1999 - Annals of Pure and Applied Logic 97 (1-3):1-25.
omnibus Review. [REVIEW]Peter Nyikos - 1992 - Journal of Symbolic Logic 57 (2):763-766.
[Omnibus Review].Peter J. Nyikos - 1992 - Journal of Symbolic Logic 57 (2):763-766.
The Causal Impact of Resistance: Mediating between Resistance and Internal Conversation about Resistance.Athanasia Chalari - 2013 - Journal for the Theory of Social Behaviour 43 (1):66-86.
Universal theories categorical in power and κ-generated models.Steven Givant & Saharon Shelah - 1994 - Annals of Pure and Applied Logic 69 (1):27-51.
Categoricity for abstract classes with amalgamation.Saharon Shelah - 1999 - Annals of Pure and Applied Logic 98 (1-3):261-294.
On some configurations related to the Shelah Weak Hypothesis.Moti Gitik & Saharon Shelah - 2001 - Archive for Mathematical Logic 40 (8):639-650.
Higher Souslin Trees and the Generalized Continuum Hypothesis.John Gregory, Richard Laver, Saharon Shelah, S. Shelah & L. Stanley - 1984 - Journal of Symbolic Logic 49 (2):663-665.

Analytics

Added to PP
2021-02-12

Downloads
9 (#1,187,161)

6 months
3 (#902,269)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Andrés Villaveces
Universidad Nacional de Colombia

Citations of this work

No citations found.

Add more citations

References found in this work

Mathematical logic.Joseph R. Shoenfield - 1967 - Reading, Mass.,: Addison-Wesley.

Add more references