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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

The Hanf number of the first order theory of Banach spaces


Authors: Saharon Shelah and Jacques Stern
Journal: Trans. Amer. Math. Soc. 244 (1978), 147-171
MSC: Primary 03C65; Secondary 46B99
MathSciNet review: 506613
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Abstract: In this paper, we discuss the possibility of developing a nice i.e. first order theory for Banach spaces: the restrictions on the set of sentences for recent compactness arguments applied to Banach spaces as well as for other model-theoretic results are both natural and necessary; without them we essentially get a second order logic with quantification over countable sets. Especially, the Hanf number for sets of sentences of the first order theory of Banach spaces is exactly the Hanf number for the second order logic of binary relations (with the second order quantifiers ranging over countable sets).


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DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0506613-3
PII: S 0002-9947(1978)0506613-3
Article copyright: © Copyright 1978 American Mathematical Society