TAMENESS FROM LARGE CARDINAL AXIOMS

DOI10.1017/jsl.2014.30zbMath1353.03023arXiv1303.0550OpenAlexW2963523306MaRDI QIDQ5177877

Will Boney

Publication date: 6 March 2015

Published in: The Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.0550

zbMATH Keywords

large cardinalstamenessabstract elementary classes

Mathematics Subject Classification ID

Large cardinals (03E55) Properties of classes of models (03C52) Abstract elementary classes and related topics (03C48)

Related Items (35)

Shelah's eventual categoricity conjecture in universal classes. I. ⋮ \(\mu\)-abstract elementary classes and other generalizations ⋮ Canonical forking in AECs ⋮ The joint embedding property and maximal models ⋮ Infinitary stability theory ⋮ Building independence relations in abstract elementary classes ⋮ Toward a stability theory of tame abstract elementary classes ⋮ Good frames in the Hart-Shelah example ⋮ Saturation and solvability in abstract elementary classes with amalgamation ⋮ Accessible images revisited ⋮ Tameness, uniqueness triples and amalgamation ⋮ Large cardinal axioms from tameness in AECs ⋮ Building prime models in fully good abstract elementary classes ⋮ A presentation theorem for continuous logic and metric abstract elementary classes ⋮ Shelah's eventual categoricity conjecture in tame abstract elementary classes with primes ⋮ TAMENESS AND FRAMES REVISITED ⋮ METRIC ABSTRACT ELEMENTARY CLASSES AS ACCESSIBLE CATEGORIES ⋮ EQUIVALENT DEFINITIONS OF SUPERSTABILITY IN TAME ABSTRACT ELEMENTARY CLASSES ⋮ Sizes and filtrations in accessible categories ⋮ Tameness in generalized metric structures ⋮ Forking independence from the categorical point of view ⋮ A category-theoretic characterization of almost measurable cardinals ⋮ Shelah's eventual categoricity conjecture in universal classes. II ⋮ Chains of saturated models in AECs ⋮ Symmetry in abstract elementary classes with amalgamation ⋮ Forking in short and tame abstract elementary classes ⋮ Internal sizes in \(\mu\)-abstract elementary classes ⋮ Simple-like independence relations in abstract elementary classes ⋮ Downward categoricity from a successor inside a good frame ⋮ Tameness from two successive good frames ⋮ Tameness, powerful images, and large cardinals ⋮ Categoricity in multiuniversal classes ⋮ The categoricity spectrum of large abstract elementary classes ⋮ Algebraic description of limit models in classes of abelian groups ⋮ THE KIM–PILLAY THEOREM FOR ABSTRACT ELEMENTARY CATEGORIES

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Erratum to: ``Categoricity in abstract elementary classes with no maximal models
• Categoricity over P for first order T or categoricity for \(\phi\) \(\in {\mathcal L}_{\omega_ 1\omega}\) can stop at \(\aleph_ k\) while holding for \(\aleph_ 0,\dots ,\aleph_{k-1}\)
• Categoricity, amalgamation, and tameness
• Categoricity of theories in \(L_{\kappa \omega}\), with \(\kappa\) a compact cardinal
• Categoricity in homogeneous complete metric spaces
• Toward categoricity for classes with no maximal models
• Categoricity in abstract elementary classes with no maximal models
• Categoricity of theories in L_{κ^*, ω}, when κ^*is a measurable cardinal. Part 2
• CATEGORICITY FROM ONE SUCCESSOR CARDINAL IN TAME ABSTRACT ELEMENTARY CLASSES
• Superstability in simple finitary AECs
• GALOIS-STABILITY FOR TAME ABSTRACT ELEMENTARY CLASSES

This page was built for publication: TAMENESS FROM LARGE CARDINAL AXIOMS