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Petr Hájek, A non-arithmetical Gödel logic, Logic Journal of the IGPL, Volume 13, Issue 4, July 2005, Pages 435–441, https://doi.org/10.1093/jigpal/jzi033
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Abstract
The logic in question is G↓ – Gödel predicate logic with the set of truth values being V↓ = {1/n | n = 1, 2, …} ∪ {0}. It is shown in [1] that the set of its tautologies is not recursively axiomatizable (is Π1-hard). We show that this set is even non-arithmetical and (before this) we prove the set of satisfiable formulas of G↓ to be non-arithmetical. In the last section we show that another important Gödel logic G↑ is arithmetical, more precisely, its set of tautologies is Π2-complete.
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© The Author, 2005. Published by Oxford University Press. All rights reserved.
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