Multimo dal Logics of Products of Topologies |
| |
| Authors: | J. van Benthem G. Bezhanishvili B. ten Cate D. Sarenac |
| |
| Affiliation: | (1) ILLC, University of Amsterdam, Plantage Muidergracht 24, 1018 TV AMSTERDAM, Netherlands;(2) Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003, USA;(3) ISLA, University of Amsterdam, Kruislaan 403, 1098 SJ Amsterdam, Netherlands;(4) Department of Philosophy, Stanford University, Stanford, CA 94305, USA |
| |
| Abstract: | We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion S4 ⊕ S4. We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies.We prove that both of these logics are complete for the product of rational numbers ℚ × ℚ with the appropriate topologies. AMS subject classification : 03B45, 54B10 The last author’s research was supported by a Social Sciences and Humanities Research Council of Canada grant number: 725-2000-2237. Presented by Melvin Fitting |
| |
| Keywords: | Fusion of modal logics products of modal logics topological product horizontal vertical topologies |
| 本文献已被 SpringerLink 等数据库收录！ |
|
