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 \(\aleph_ 0,\dots ,\aleph_{k-1}\)

DOI10.1007/BF02807869zbMath0723.03017arXivmath/9201240OpenAlexW1978825183MaRDI QIDQ757348

Saharon Shelah, Bradd Hart

Publication date: 1990

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9201240

zbMATH Keywords

relative categoricity

Mathematics Subject Classification ID

Other infinitary logic (03C75) Categoricity and completeness of theories (03C35)

Related Items (30)

Shelah's eventual categoricity conjecture in universal classes. I. ⋮ Infinitary stability theory ⋮ Categoricity, amalgamation, and tameness ⋮ Categoricity transfer in simple finitary abstract elementary classes ⋮ Beginning of stability theory for Polish spaces ⋮ Abstract elementary classes stable in \(\aleph_{0}\) ⋮ Good frames in the Hart-Shelah example ⋮ ON CATEGORICITY IN SUCCESSIVE CARDINALS ⋮ Saturation and solvability in abstract elementary classes with amalgamation ⋮ The Hart-Shelah example, in stronger logics ⋮ TAMENESS AND FRAMES REVISITED ⋮ Omega-categoricity, relative categoricity and coordinatisation ⋮ Structural logic and abstract elementary classes with intersections ⋮ UNIVERSAL CLASSES NEAR ${\aleph _1}$ ⋮ Forking in short and tame abstract elementary classes ⋮ Main gap for locally saturated elementary submodels of a homogeneous structure ⋮ Polish algebras, shy from freedom. ⋮ DISJOINT AMALGAMATION IN LOCALLY FINITE AEC ⋮ Tameness and extending frames ⋮ TAMENESS FROM LARGE CARDINAL AXIOMS ⋮ Notes on Quasiminimality and Excellence ⋮ Categoricity in abstract elementary classes with no maximal models ⋮ Categoricity of an abstract elementary class in two successive cardinals ⋮ Downward categoricity from a successor inside a good frame ⋮ Symmetry and the union of saturated models in superstable abstract elementary classes ⋮ Relative categoricity in abelian groups. II ⋮ Tameness from two successive good frames ⋮ Shelah's categoricity conjecture from a successor for tame abstract elementary classes ⋮ The categoricity spectrum of large abstract elementary classes ⋮ Type-amalgamation properties and polygroupoids in stable theories

Cites Work

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• Omega-categoricity, relative categoricity and coordinatisation
• Classification theory over a predicate. I
• Around classification theory of models
• \(\aleph_0\)-categoricity over a predicate
• A minimal prime model with an infinite set of indiscernibles
• Categoricity in \(\aleph_1\) of sentences in \(L_{\omega_1\omega}(Q)\)
• Model theory for infinitary logic. Logic with countable conjunctions and finite quantifiers
• K. Tent and M. Ziegler. A Course in Model Theory. Lecture Notes in Logic, vol. 40. Cambridge University Press, United Kingdom, 2012, x + 248 pp.
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