Categoricity of theories in Lκω , when κ is a measurable cardinal. Part 1
Fundamenta Mathematicae (1996)
- Volume: 151, Issue: 3, page 209-240
- ISSN: 0016-2736
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topShelah, Saharon, and Kolman, Oren. "Categoricity of theories in Lκω , when κ is a measurable cardinal. Part 1." Fundamenta Mathematicae 151.3 (1996): 209-240. <http://eudml.org/doc/212193>.
@article{Shelah1996,
abstract = {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.},
author = {Shelah, Saharon, Kolman, Oren},
journal = {Fundamenta Mathematicae},
keywords = {categoricity; classification theory in nonelementary classes; amalgamation property},
language = {eng},
number = {3},
pages = {209-240},
title = {Categoricity of theories in Lκω , when κ is a measurable cardinal. Part 1},
url = {http://eudml.org/doc/212193},
volume = {151},
year = {1996},
}
TY - JOUR
AU - Shelah, Saharon
AU - Kolman, Oren
TI - Categoricity of theories in Lκω , when κ is a measurable cardinal. Part 1
JO - Fundamenta Mathematicae
PY - 1996
VL - 151
IS - 3
SP - 209
EP - 240
AB - 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.
LA - eng
KW - categoricity; classification theory in nonelementary classes; amalgamation property
UR - http://eudml.org/doc/212193
ER -
References
top- [CK] C. C. Chang and H. J. Keisler, Model Theory, North-Holland, 1973.
- [D] M. Dickmann, Large Infinitary Languages: Model Theory, North-Holland, 1975. Zbl0324.02010
- [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 can stop at while holding for , 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. Zbl0501.03014
- [J] T. Jech, Set Theory, Academic Press, 1978.
- [K] H. J. Keisler, Model Theory for Infinitary Logic, North-Holland, 1971. Zbl0222.02064
- [L] R. Laver, On Fraïssé's order type conjecture, Ann. of Math. 93 (1971), 89-111. Zbl0208.28905
- [MaSh285] M. Makkai and S. Shelah, Categoricity of theories in , with κ a compact cardinal, Ann. Pure Appl. Logic 47 (1990), 41-97. Zbl0704.03015
- [M] M. Morley, Categoricity in power, Trans. Amer. Math. Soc. 114 (1965), 514-518. Zbl0151.01101
- [N] M. Nadel, 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. Zbl0209.30403
- [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. Zbl0193.30002
- [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 of sentences in , Israel J. Math. 20 (1975), 127-148.
- [Sh87] S. Shelah, Classification theory for non-elementary classes I: The number of uncountable models of , 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 -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.
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