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JSYML

2010

2010

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 ...

Related Content

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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