On categoricity in successive cardinals

Journal of Symbolic Logic:1-19 (2020)
  Copy   BIBTEX

Abstract

We investigate, in ZFC, the behavior of abstract elementary classes categorical in many successive small cardinals. We prove for example that a universal $\mathbb {L}_{\omega _1, \omega }$ sentence categorical on an end segment of cardinals below $\beth _\omega $ must be categorical also everywhere above $\beth _\omega $. This is done without any additional model-theoretic hypotheses and generalizes to the much broader framework of tame AECs with weak amalgamation and coherent sequences.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,616

External links

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

Through your library

Similar books and articles

Tameness from large cardinal axioms.Will Boney - 2014 - Journal of Symbolic Logic 79 (4):1092-1119.
Strong tree properties for two successive cardinals.Laura Fontanella - 2012 - Archive for Mathematical Logic 51 (5-6):601-620.
On an application of categoricity.Alexander Paseau - 2005 - Proceedings of the Aristotelian Society 105 (3):411–415.
Categoricity Spectra for Rigid Structures.Ekaterina Fokina, Andrey Frolov & Iskander Kalimullin - 2016 - Notre Dame Journal of Formal Logic 57 (1):45-57.
Successive weakly compact or singular cardinals.Ralf-Dieter Schindler - 1999 - Journal of Symbolic Logic 64 (1):139-146.
Categoricity and indefinite extensibility.James Walmsley - 2002 - Proceedings of the Aristotelian Society 102 (3):217–235.
Degrees That Are Not Degrees of Categoricity.Bernard Anderson & Barbara Csima - 2016 - Notre Dame Journal of Formal Logic 57 (3):389-398.
Gap forcing: Generalizing the lévy-Solovay theorem.Joel David Hamkins - 1999 - Bulletin of Symbolic Logic 5 (2):264-272.
Successive large cardinals.Everett L. Bull - 1978 - Annals of Mathematical Logic 15 (2):161.

Analytics

Added to PP
2020-07-21

Downloads
8 (#1,138,312)

6 months
3 (#445,838)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

Galois-stability for Tame abstract elementary classes.Rami Grossberg & Monica Vandieren - 2006 - Journal of Mathematical Logic 6 (01):25-48.
Categoricity for abstract classes with amalgamation.Saharon Shelah - 1999 - Annals of Pure and Applied Logic 98 (1-3):261-294.
Shelah's eventual categoricity conjecture in universal classes: Part I.Sebastien Vasey - 2017 - Annals of Pure and Applied Logic 168 (9):1609-1642.
Tameness and extending frames.Will Boney - 2014 - Journal of Mathematical Logic 14 (2):1450007.
Toward categoricity for classes with no maximal models.Saharon Shelah & Andrés Villaveces - 1999 - Annals of Pure and Applied Logic 97 (1-3):1-25.

View all 12 references / Add more references