Skip to main content
    • Aa
    • Aa


  • WILL BONEY (a1)

We show that Shelah’s Eventual Categoricity Conjecture for successors follows from the existence of class many strongly compact cardinals. This is the first time the consistency of this conjecture has been proven. We do so by showing that every AEC with LS(K) below a strongly compact cardinal κ is < κ-tame and applying the categoricity transfer of Grossberg and VanDieren [11]. These techniques also apply to measurable and weakly compact cardinals and we prove similar tameness results under those hypotheses. We isolate a dual property to tameness, called type shortness, and show that it follows similarly from large cardinals.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

John Baldwin and Alexei Kolesnikov , Categoricity, amalgamation, and tameness. Israel Journal of Mathematics, vol. 170 (2009), no. 1, pp. 411443.

Will Boney , Rami Grossberg , Alexei Kolesnikov , and Sebastien Vasey , Canonical Forking in AECs, Submitted, arXiv: 1404.1494.

C. C. Chang , Some remarks on the model theory of infinitary languages, The Syntax and Semantics of Infinitary Languages ( J. Barwise , editor), vol.72, Springer-Verlag Lecture Notes in Mathematics, 1968, pp. 3663.

Paul Ekloff and Alan Mekler , Almost Free Modules: Set-Theoretic Methods, Elsevier, Amsterdam, 2002.

Rami Grossberg and Monica VanDieren , Categoricity from one successor cardinal in tame Abstract Elementary Classes. Journal of Mathematical Logic, vol. 6 (2006), no. 2, pp. 181201.

Rami Grossberg , Galois-stability for tame Abstract Elementary Classes.Journal of Mathematical Logic, vol. 6 (2006), no. 1, pp. 2549.

Åsa Hirvonen and Tapani Hyttinen , Categoricity in homogeneous complete metric spaces. Archive of Mathematical Logic, vol. 48 (2009), no. 3-4, pp. 269322.

Tapani Hyttinen and Meeri Kesälä , Superstability in simple finitary AECs. Fundamenta Mathematica, vol. 195 (2007), no. 3, pp. 221268.

Saharon Shelah and Michael Makkai , Categoricity of theories inLκω, with κ a compact cardinal. Annals of Pure and Applied Logic, vol. 47 (1990), pp. 4197.

Menachem Magidor and Saharon Shelah , When does almost free imply free? (for groups, transversals, etc.). Journal of the American Mathematical Society, vol. 7 (1994), pp. 769830.

M. Morley , Categoricity in power. Transactions of the American Mathematical Society, vol. 114 (1965), pp. 514538.

Saharon Shelah and Andres Villaveces , Toward categoricity for classes with no maximal models. Annals of Pure and Applied Logic, vol. 97 (1999), pp. 125.

Monica VanDieren , Categoricity in Abstract Elementary Classes with no maximal models. Annals of Pure and Applied Logic, vol. 141 (2006), pp. 108147.

Monica VanDieren , Erratum to “Categoricity in Abstract Elementary Classes with no maximal models”. Annals of Pure and Applied Logic, vol. 164 (2013), pp. 131133.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 11 *
Loading metrics...

Abstract views

Total abstract views: 103 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 23rd September 2017. This data will be updated every 24 hours.