The Σ1-provability logic of HA
| Autor: | Mohammad Ardeshir, S. Mojtaba Mojtahedi |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Discrete mathematics
Property (philosophy) Logic 010102 general mathematics Provability logic 02 engineering and technology 01 natural sciences Decidability Modal theory 0202 electrical engineering electronic engineering information engineering Arithmetic function 020201 artificial intelligence & image processing 0101 mathematics Mathematics |
| Zdroj: | Annals of Pure and Applied Logic. 169:997-1043 |
| ISSN: | 0168-0072 |
| DOI: | 10.1016/j.apal.2018.05.001 |
| Popis: | In this paper we introduce a modal theory iH σ which is sound and complete for arithmetical Σ 1 -interpretations in HA , in other words, we will show that iH σ is the Σ 1 -provability logic of HA . Moreover we will show that iH σ is decidable. As a by-product of these results, we show that HA + □ ⊥ has de Jongh property. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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