M. Fujiwara, H. Ishihara, Takako Nemoto, Nobu-Yuki Suzuki, K. Yokoyama
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EXTENDED FRAMES AND SEPARATIONS OF LOGICAL PRINCIPLES
Abstract 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.