Journal of Mathematical Logic 3 (01):85-118 (2003)

Abstract
We develop positive model theory, which is a non first order analogue of classical model theory where compactness is kept at the expense of negation. The analogue of a first order theory in this framework is a compact abstract theory: several equivalent yet conceptually different presentations of this notion are given. We prove in particular that Banach and Hilbert spaces are compact abstract theories, and in fact very well-behaved as such.
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DOI 10.1142/S0219061303000212
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References found in this work BETA

Categoricity for Abstract Classes with Amalgamation.Saharon Shelah - 1999 - Annals of Pure and Applied Logic 98 (1-3):261-294.
Simplicity in Compact Abstract Theories.Itay Ben-Yaacov - 2003 - Journal of Mathematical Logic 3 (02):163-191.

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Citations of this work BETA

Simplicity in Compact Abstract Theories.Itay Ben-Yaacov - 2003 - Journal of Mathematical Logic 3 (02):163-191.
Positive Jonsson Theories.Bruno Poizat & Aibat Yeshkeyev - 2018 - Logica Universalis 12 (1-2):101-127.
Lovely Pairs of Models.Itay Ben-Yaacov, Anand Pillay & Evgueni Vassiliev - 2003 - Annals of Pure and Applied Logic 122 (1-3):235-261.

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