The hanf number of the first order theory of banach spaces

Saharon Shelah, Jacques Stern

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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).

Original languageEnglish
Pages (from-to)147-171
Number of pages25
JournalTransactions of the American Mathematical Society
Volume244
DOIs
StatePublished - Oct 1978

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