TY - JOUR
T1 - The hanf number of the first order theory of banach spaces
AU - Shelah, Saharon
AU - Stern, Jacques
PY - 1978/10
Y1 - 1978/10
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=84968486202&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-1978-0506613-3
DO - 10.1090/S0002-9947-1978-0506613-3
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AN - SCOPUS:84968486202
SN - 0002-9947
VL - 244
SP - 147
EP - 171
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
ER -