Abstract
AbstractWe prove a topological completeness theorem for the modal logic $$\textsf{GLP}$$
GLP
containing operators $$\{\langle \xi \rangle :\xi \in \textsf{Ord}\}$$
{
⟨
ξ
⟩
:
ξ
∈
Ord
}
intended to capture a wellordered sequence of consistency operators increasing in strength. More specifically, we prove that, given a tall-enough scattered space X, any sentence $$\phi $$
ϕ
consistent with $$\textsf{GLP}$$
GLP
can be satisfied on a polytopological space based on finitely many Icard topologies constructed over X and corresponding to the finitely many modalities that occur in $$\phi $$
ϕ
.
Publisher
Springer Science and Business Media LLC
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