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An arithmetical view to first-order logic |
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| Authors: | Seyed Mohammad Bagheri Bruno Poizat |
| Affiliation: | a Department of Mathematics, Tarbiat Modares University, Tehran, P.O. Box 14115-175, Iran b Institut Camille Jordan, Université Claude Bernard, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne-cedex, France c Department of Mathematics, Amirkabir University of Technology, Tehran, P.O. Box 15875-4413, Iran |
| Abstract: | A value space is a topological algebra B equipped with a non-empty family of continuous quantifiers  :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. |
| Keywords: | 03C80 03C95 |
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