1 results
EXTENDED FRAMES AND SEPARATIONS OF LOGICAL PRINCIPLES
- Part of
-
- Journal:
- Bulletin of Symbolic Logic / Volume 29 / Issue 3 / September 2023
- Published online by Cambridge University Press:
- 26 July 2023, pp. 311-353
- Print publication:
- September 2023
-
- Article
-
- You have access
- HTML
- Export citation
-
We aim at developing a systematic method of separating omniscience principles by constructing Kripke models for intuitionistic predicate logic
$\mathbf {IQC}$ and first-order arithmetic 
$\mathbf {HA}$ from a Kripke model for intuitionistic propositional logic 
$\mathbf {IPC}$. To this end, we introduce the notion of an extended frame, and show that each IPC-Kripke model generates an extended frame. By using the extended frame generated by an IPC-Kripke model, we give a separation theorem of a schema from a set of schemata in 
$\mathbf {IQC}$ and a separation theorem of a sentence from a set of schemata in 
$\mathbf {HA}$. We see several examples which give us separations among omniscience principles.
