PP-2022-03: van Benthem, Johan and Bezhanishvili, Nick (2022) Modal structures in groups and vector spaces. [Pre-print]
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Abstract
Vector spaces show a number of general structures that invite analysis in modal logics.
As such, they provide an interesting counterpart to the much better-studied modal logics of topology. At the same time, vector spaces pose several challenges to this style of analysis of a mathematical practice. In this programmatic paper, we present a number of modal logics of groups and then full fledged vector spaces, including some new logics of dependence and independence. In particular, we investigate issues of definability and axiomatization using standard techniques for modal and hybrid languages. Our discussion identifies several leads for more systematic research.
| Item Type: | Pre-print |
|---|---|
| Report Nr: | PP-2022-03 |
| Series Name: | Prepublication (PP) Series |
| Year: | 2022 |
| Subjects: | Computation Logic Mathematics |
| Depositing User: | Nick Bezhanishvili |
| Date Deposited: | 10 Mar 2022 20:28 |
| Last Modified: | 19 Mar 2023 13:52 |
| URI: | https://eprints.illc.uva.nl/id/eprint/1871 |
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