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  1.  23
    Consistency of Heyting Arithmetic in Natural Deduction.Annika Kanckos - 2010 - Mathematical Logic Quarterly 56 (6):611-624.
    A proof of the consistency of Heyting arithmetic formulated in natural deduction is given. The proof is a reduction procedure for derivations of falsity and a vector assignment, such that each reduction reduces the vector. By an interpretation of the expressions of the vectors as ordinals each derivation of falsity is assigned an ordinal less than ε 0, thus proving termination of the procedure.
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  2.  13
    A Note on Gentzen’s Ordinal Assignment.Annika Kanckos - 2019 - Archive for Mathematical Logic 58 (3-4):347-352.
    Gentzen’s height measure of the 1938 consistency proof is a cumulative complexity measure for sequents that is measured bottom-up in a derivation. By a factorisation of the ordinal assignment a top-down ordinal assignment can be given that does not depend on information occurring below the sequent to which the ordinal is assigned. Furthermore, an ordinal collapsing function is defined in order to collapse the top-down ordinal to the one assigned by Gentzen’s own ordinal assignment. A direct definition of the factorised (...)
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  3.  19
    The Development of Gödel’s Ontological Proof.Annika Kanckos & Tim Lethen - forthcoming - Review of Symbolic Logic:1-19.
    Gödel’s ontological proof is by now well known based on the 1970 version, written in Gödel’s own hand, and Scott’s version of the proof. In this article new manuscript sources found in Gödel’s Nachlass are presented. Three versions of Gödel’s ontological proof have been transcribed, and completed from context as true to Gödel’s notes as possible. The discussion in this article is based on these new sources and reveals Gödel’s early intentions of a liberal comprehension principle for the higher order (...)
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  4.  19
    Variants of Gödel’s Ontological Proof in a Natural Deduction Calculus.B. Woltzenlogel Paleo & Annika Kanckos - 2017 - Studia Logica 105 (3):553-586.
    This paper presents detailed formalizations of ontological arguments in a simple modal natural deduction calculus. The first formal proof closely follows the hints in Scott’s manuscript about Gödel’s argument and fills in the gaps, thus verifying its correctness. The second formal proof improves the first one, by relying on the weaker modal logic KB instead of S5 and by avoiding the equality relation. The second proof is also technically shorter than the first one, because it eliminates unnecessary detours and uses (...)
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