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Strong completeness of provability logic for ordinal spaces

(2017) JOURNAL OF SYMBOLIC LOGIC. 82(2). p.608-628
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Abstract
Given a scattered space (sic) = ((sic), tau) and an ordinal lambda, we define a topology tau(+lambda) in such a way that tau(+0) = tau and, when (sic) is an ordinal with the initial segment topology, the resulting sequence {tau(+lambda)}(lambda is an element of Ord) coincides with the family of topologies {I-lambda}(lambda is an element of Ord) used by Icard, Joosten, and the second author to provide semantics for polymodal provability logics. We prove that given any scattered space (sic) of large-enough rank and any ordinal lambda > 0, GL is strongly complete for tau(+lambda). The special case where (sic) = omega(omega) + 1 and lambda = 1 yields a strengthening of a theorem of Abashidze and Blass.
Keywords
provability logic, topological semantics, scattered space, GLP

Citation

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MLA
Aguilera, Juan P, and David Fernández-Duque. “Strong Completeness of Provability Logic for Ordinal Spaces.” JOURNAL OF SYMBOLIC LOGIC 82.2 (2017): 608–628. Print.
APA
Aguilera, J. P., & Fernández-Duque, D. (2017). Strong completeness of provability logic for ordinal spaces. JOURNAL OF SYMBOLIC LOGIC, 82(2), 608–628.
Chicago author-date
Aguilera, Juan P, and David Fernández-Duque. 2017. “Strong Completeness of Provability Logic for Ordinal Spaces.” Journal of Symbolic Logic 82 (2): 608–628.
Chicago author-date (all authors)
Aguilera, Juan P, and David Fernández-Duque. 2017. “Strong Completeness of Provability Logic for Ordinal Spaces.” Journal of Symbolic Logic 82 (2): 608–628.
Vancouver
1.
Aguilera JP, Fernández-Duque D. Strong completeness of provability logic for ordinal spaces. JOURNAL OF SYMBOLIC LOGIC. 2017;82(2):608–28.
IEEE
[1]
J. P. Aguilera and D. Fernández-Duque, “Strong completeness of provability logic for ordinal spaces,” JOURNAL OF SYMBOLIC LOGIC, vol. 82, no. 2, pp. 608–628, 2017.
@article{8566404,
  abstract     = {Given a scattered space (sic) = ((sic), tau) and an ordinal lambda, we define a topology tau(+lambda) in such a way that tau(+0) = tau and, when (sic) is an ordinal with the initial segment topology, the resulting sequence {tau(+lambda)}(lambda is an element of Ord) coincides with the family of topologies {I-lambda}(lambda is an element of Ord) used by Icard, Joosten, and the second author to provide semantics for polymodal provability logics. 
We prove that given any scattered space (sic) of large-enough rank and any ordinal lambda > 0, GL is strongly complete for tau(+lambda). The special case where (sic) = omega(omega) + 1 and lambda = 1 yields a strengthening of a theorem of Abashidze and Blass.},
  author       = {Aguilera, Juan P and Fernández-Duque, David},
  issn         = {0022-4812},
  journal      = {JOURNAL OF SYMBOLIC LOGIC},
  keywords     = {provability logic,topological semantics,scattered space,GLP},
  language     = {eng},
  number       = {2},
  pages        = {608--628},
  title        = {Strong completeness of provability logic for ordinal spaces},
  url          = {http://dx.doi.org/10.1017/jsl.2017.3},
  volume       = {82},
  year         = {2017},
}

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