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- W3020614086 abstract "Abstract We prove a topological completeness theorem for the modal logic $$textsf{GLP}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>GLP</mml:mi> </mml:math> containing operators $${langle xi rangle :xi in textsf{Ord}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mo>{</mml:mo> <mml:mo>⟨</mml:mo> <mml:mi>ξ</mml:mi> <mml:mo>⟩</mml:mo> <mml:mo>:</mml:mo> <mml:mi>ξ</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>Ord</mml:mi> <mml:mo>}</mml:mo> </mml:mrow> </mml:math> 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 $$phi $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>ϕ</mml:mi> </mml:math> consistent with $$textsf{GLP}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>GLP</mml:mi> </mml:math> 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 $$phi $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>ϕ</mml:mi> </mml:math> ." @default.
- W3020614086 created "2020-05-01" @default.
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- W3020614086 date "2023-02-22" @default.
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- W3020614086 title "A topological completeness theorem for transfinite provability logic" @default.
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- W3020614086 doi "https://doi.org/10.1007/s00153-023-00863-9" @default.
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