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1996 | 151 | 3 | 209-240
Tytuł artykułu

Categoricity of theories in Lκω , when κ is a measurable cardinal. Part 1

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We assume a theory T in the logic $L_{κω}$ is categorical in a cardinal λ \≥ κ, and κ is a measurable cardinal. We prove that the class of models of T of cardinality < λ (but ≥ |T|+κ) has the amalgamation property; this is a step toward understanding the character of such classes of models.
Słowa kluczowe
Kategorie tematyczne
Rocznik
Tom
151
Numer
3
Strony
209-240
Opis fizyczny
Daty
wydano
1996
otrzymano
1994-02-02
poprawiono
1996-02-08
Twórcy
autor
  • Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903, U.S.A.
Bibliografia
  • [CK] C. C. Chang and H. J. Keisler, Model Theory, North-Holland, 1973.
  • [D] M. Dickmann, Large Infinitary Languages: Model Theory, North-Holland, 1975.
  • [D1] M. Dickmann, Larger infinitary languages, Chapter IX of Model-Theoretic Logics, J. Barwise and S. Feferman (eds.), Perspect. Math. Logic, Springer, New York, 1985, 317-363.
  • [HaSh323] B. Hart and S. Shelah, Categoricity over P for first order T or categoricity for $φ ∈ L_ω_1ω$ can stop at $ℵ_k$ while holding for $ℵ_0,...,ℵ_k-1$, Israel J. Math. 70 (1990), 219-235.
  • [HoSh109] W. Hodges and S. Shelah, Infinite games and reduced products, Ann. Math. Logic 20 (1981), 77-108.
  • [J] T. Jech, Set Theory, Academic Press, 1978.
  • [K] H. J. Keisler, Model Theory for Infinitary Logic, North-Holland, 1971.
  • [L] R. Laver, On Fraïssé's order type conjecture, Ann. of Math. 93 (1971), 89-111.
  • [MaSh285] M. Makkai and S. Shelah, Categoricity of theories in $L_{κw}$, with κ a compact cardinal, Ann. Pure Appl. Logic 47 (1990), 41-97.
  • [M] M. Morley, Categoricity in power, Trans. Amer. Math. Soc. 114 (1965), 514-518.
  • [N] M. Nadel, $L_ω_1ω$ and admissible fragments, Chapter VIII of Model-Theoretic Logics, J. Barwise and S. Feferman (eds.), Perspect. Math. Logic, Springer, New York, 1985, 271-316.
  • [Re] J. P. Ressayre, Sur les théories du premier ordre catégorique en un cardinal, Trans. Amer. Math. Soc. 142 (1969), 481-505.
  • [Ro] F. Rowbottom, The Łoś conjecture for uncountable theories, Notices Amer. Math. Soc. 11 (1964), 284.
  • [Sh2] S. Shelah, Stable theories, Israel J. Math. 7 (1969), 187-202.
  • [Sh31] S. Shelah, Solution to Łoś conjecture for uncountable languages, in: Proc. Sympos. Pure Math. 25, Amer. Math. Soc., 1974, 53-74.
  • [Sh48] S. Shelah, Categoricity in $ℵ_1$ of sentences in $L_ω_1,ω(Q)$, Israel J. Math. 20 (1975), 127-148.
  • [Sh87] S. Shelah, Classification theory for non-elementary classes I: The number of uncountable models of $ψ ∈ L_ω_1,ω$, Parts A, B, Israel J. Math. 46 (1983), 212-240, 241-273.
  • [Sh88] S. Shelah, Classification theory for non elementary classes II. Abstract elementary classes, in: Classification Theory, Proc. US-Israel Workshop on Model Theory in Mathematical Logic, Springer, 1987, 419-497.
  • [Sh220] S. Shelah, Existence of many $L_ℵ, λ$-equivalent, non-isomorphic models of T of power λ, Ann. Pure Appl. Logic 34 (1987), 291-310.
  • [Sh300] S. Shelah, Universal classes, in: Classification Theory, Proc. US-Israel Workshop on Model Theory in Mathematical Logic, Springer, 1987, 264-418.
  • [Sh420] S. Shelah, Advances in cardinal arithmetic, in: Finite and Infinite Combinatorics in Sets and Logic, N. W. Sauer et al. (eds.), Kluwer Acad. Publ., 1993, 355-383.
  • [Sh394] S. Shelah, Categoricity of abstract classes with amalgamation, preprint.
  • [Sh472] S. Shelah, Categoricity for infinitary logics II, Fund. Math., submitted.
  • [Sh576] S. Shelah, On categoricity of abstract elementary classes: in three cardinals imply existence of a model of the next, preprint.
  • [Sh600] S. Shelah, Continuation of [Sh576], in preparation.
  • [Sh600] S. Shelah, Classification Theory and the Number of Non-Isomorphic Models, North-Holland, 1978.
  • [Sh-a] S. Shelah, Classification Theory and the Number of Non-Isomorphic Models, Classification Theory and the Number of Non-Isomorphic Models, revised, Stud. Logic Found. Math. 92, North-Holland, 1990.
  • [Sh-h] S. Shelah, Classification Theory and the Number of Non-Isomorphic Models, Universal classes, preprint.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv151i3p209bwm
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