Categoricity in Abstract Elementary Classes: Going up Inductive Step Sh600 -part 1 and 2

@inproceedings{ShelahCategoricityIA,
  title={Categoricity in Abstract Elementary Classes: Going up Inductive Step Sh600 -part 1 and 2},
  author={Saharon Shelah}
}
We deal with beginning stability theory for " reasonable " non-elementary classes without any remnants of compactness like dealing with models above Hanf number or by the class being definable by L ω 1 ,ω. We introduce and investigate good λ-frame, show that they can be found under reasonable assumptions and prove we can advance from λ to λ + when non-structure fail. That is, assume 2 λ +n < 2 λ +n+1 for n < ω. So if an a.e.c. is cateogorical in λ, λ + and has intermediate number of models in… CONTINUE READING

From This Paper

Topics from this paper.
6 Citations
27 References
Similar Papers

References

Publications referenced by this paper.
Showing 1-10 of 27 references

Sh 576] Saharon Shelah Categoricity of an abstract elementary class in two successive cardinals

  • Israel Journal of Mathematics
  • 2001

Sh:c] Saharon Shelah. Classification theory and the number of nonisomorphic models, volume 92 of Studies in Logic and the Foundations of Mathematics

  • Sh:c] Saharon Shelah. Classification theory and…
  • 1990

HuSh 342] Ehud Hrushovski and Saharon Shelah. A dichotomy theorem for regular types

  • Annals of Pure and Applied Logic
  • 1989

Classification of nonelementary classes. II. Abstract elementary classes

  • Sh 88 ] Saharon Shelah Ed, J T Baldwin
  • Classification theory Proceedings of the USA…
  • 1985

Universal classes

  • Sh 300 ] Saharon Shelah Ed, J Baldwin
  • Classification theory Proceedings of the USA…
  • 1985

Sh 87a] Saharon Shelah. Classification theory for nonelementary classes, I. The number of uncountable models of ψ ∈ L ω 1 ,ω . Part A

  • Israel Journal of Mathematics
  • 1983

Sh 87b] Saharon Shelah. Classification theory for nonelementary classes, I. The number of uncountable models of ψ ∈ L ω 1 ,ω

  • Part B. Israel Journal of Mathematics
  • 1983

Sh 48] Saharon Shelah Categoricity in ℵ 1 of sentences in L ω 1 ,ω (Q)

  • Israel Journal of Mathematics
  • 1975

Model theory for infinitary logic. Logic with countable conjunctions and finite quantifiers, volume 62 of Studies in Logic and the Foundations of Mathematics

  • Jerome Keisler
  • Model theory for infinitary logic. Logic with…
  • 1971

1) Follows by 6.34, NF λ satisfies clauses (a)+(b) and by 6.31 it satisfies also clause (c) of Definition 6

  • 1) Follows by 6.34, NF λ satisfies clauses (a)+(b…

Similar Papers

Loading similar papers…