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JSYML
2010

A proof of completeness for continuous first-order logic

9 years 9 months ago
A proof of completeness for continuous first-order logic
Continuous first-order logic has found interest among model theorists who wish to extend the classical analysis of “algebraic” structures (such as fields, group, and graphs) to various natural classes of complete metric structures (such as probability algebras, Hilbert spaces, and Banach spaces). With research in continuous first-order logic preoccupied with studying the model theory of this framework, we find a natural question calls for attention: Is there an interesting set of axioms yielding a completeness result? The primary purpose of this article is to show that a certain, interesting set of axioms does indeed yield a completeness result for continuous first-order logic. In particular, we show that in continuous first-order logic a set of formulae is (completely) satisfiable if (and only if) it is consistent. From this result it follows that continuous first-order logic also satisfies an approximated form of strong completeness, whereby Σ ϕ (if and) only if Σ ϕ ...
Arthur Paul Pedersen, Itay Ben-Yaacov
Added 29 Jan 2011
Updated 29 Jan 2011
Type Journal
Year 2010
Where JSYML
Authors Arthur Paul Pedersen, Itay Ben-Yaacov
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