MoL-2003-01: Some Intuitionistic Provability and Preservativity Logics (and their interrelations)

MoL-2003-01: Zhou, Chunlai (2003) Some Intuitionistic Provability and Preservativity Logics (and their interrelations). [Report]

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This thesis is about the preservativity logic and provability logic of Heyting arithmetic (or HA). Our interests in this thesis are not about iPH or iH itself but about some natural sub-logical systems of iPH and iH. We attain some conservation results relating these preservativity and provability logics. Also we show the fixed point theorem for iL and iPL. There is an open question: is there an elegant axiomatization of the L2-fragment of iPH. So if the conjecture that iPH is the preservativity logic is true, then that axiomatization will be the intuitionistic provability logic, or the provability logic of HA. Although we will not answer this profound question in this thesis, the conservation results that we achieve here will contribute to our understanding of the close relation between the preservativity logic and the provability logic of HA. In fact, those conservation results are closely related to some much more intuitive equivalence results.

Item Type: Report
Report Nr: MoL-2003-01
Series Name: Master of Logic Thesis (MoL) Series
Year: 2003
Uncontrolled Keywords: Provability Logic, Preservativity Logic, Heyting Arithmetic,
Date Deposited: 12 Oct 2016 14:38
Last Modified: 12 Oct 2016 14:38

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