Uncountable dense categoricity in cats
Itay Ben-Yaacov
Source: J. Symbolic Logic Volume 70, Issue 3
(2005), 829-860.
Abstract
We prove that under reasonable assumptions, every cat (compact abstract theory) is metric, and develop some of the theory of metric cats. We generalise Morley's theorem: if a countable Hausdorff cat T has a unique complete model of density character λ ≥ ω₁, then it has a unique complete model of density character λ for every λ ≥ ω₁.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1122038916
Digital Object Identifier: doi:10.2178/jsl/1122038916
Mathematical Reviews number (MathSciNet): MR2155268
Zentralblatt MATH identifier: 1084.03028
References
Itay Ben-Yaacov Positive model theory and compact abstract theories, Journal of Mathematical Logic, vol. 3 (2003), no. 1, pp. 85--118.
Mathematical Reviews (MathSciNet): MR1978944
Digital Object Identifier: doi:10.1142/S0219061303000212
Zentralblatt MATH: 1028.03034
Bradd Hart, Byunghan Kim, and Anand Pillay Coordinatisation and canonical bases in simple theories, Journal of Symbolic Logic, vol. 65 (2000), pp. 293--309.
Mathematical Reviews (MathSciNet): MR1782121
JSTOR: links.jstor.org
C. Ward Henson Nonstandard hulls of banach spaces, Israel Journal of Mathematics, vol. 25 (1976), pp. 108--144.
Mathematical Reviews (MathSciNet): MR461104
C. Ward Henson and José Iovino Ultraproducts in analysis, Analysis and logic (Catherine Finet and Christian Michaux, editors), London Mathematical Society Lecture Notes Series, no. 262, Cambridge University Press,2002.
Mathematical Reviews (MathSciNet): MR1967834
Zentralblatt MATH: 1026.46007
José Iovino The morley rank of a banach space, Journal of Symbolic Logic, vol. 61 (1996), no. 3, pp. 928--941.
Mathematical Reviews (MathSciNet): MR1412518
JSTOR: links.jstor.org
Byunghan Kim and Anand Pillay Simple theories, Annals of Pure and Applied Logic, vol. 88 (1997), pp. 149--164.
Mathematical Reviews (MathSciNet): MR1600895
Digital Object Identifier: doi:10.1016/S0168-0072(97)00019-5
Zentralblatt MATH: 0897.03036
Bruno Poizat Cours de théorie des modèles, Nur al-Mantiq wal-Ma'rifah,1985.
Mathematical Reviews (MathSciNet): MR817208
Saharon Shelah The lazy model-theoretician's guide to stability, Logique et Analyse, vol. 71--72 (1975), pp. 241--308.
Mathematical Reviews (MathSciNet): MR539969
