An arithmetical view to first-order logic

作者：Bagheri Seyed Mohammad^*; Poizat Bruno; Pourmahdian Massoud

来源：Annals of Pure and Applied Logic, 2010, 161(6): 745-755.

DOI：10.1016/j.apal.2009.06.006

• Continuous quantifier
• Canon
• Value space
• Ultraproduct
• Representation

A value space is a topological algebra B equipped with a non-empty family of continuous quantifiers D : B* -> B. We will describe first-order logic on the basis of B. Operations of B are used as connectives and its relations are used to define statements. We prove under some normality conditions on the value space that any theory in the new setting can be represented by a classical first-order theory.

• 出版日期2010-3