Salvato in:
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| Natura: | Preprint |
| Pubblicazione: |
2017
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/1712.00317 |
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Sommario:
- The computable model theory of modal logic was initiated by Suman Ganguli and Anil Nerode in [4]. They use an effective Henkin-type construction to effectivize various completeness theorems from classical modal logic. This construction has the feature of only producing models whose frames can be obtained by adding edges to a tree digraph. Consequently, this construction cannot prove an effective version of a well-known completeness theorem which states that every $\mathsf{S4.3.1}$-theory has a model whose accessibility relation is a linear order of order type $ω$. We prove an effectivization of that theorem by means of a new construction adapted from that of Ganguli and Nerode.