Zoekopdracht:
faculteit: "FNWI" en publicatiejaar: "2003"
| Auteur | Chunlai Zhou | | Titel | Some Intuitionistic Provability and Preservativity Logics (and their interrelations) |
| Jaar | 2003 |
| Faculteit | Faculteit der Natuurwetenschappen, Wiskunde en Informatica |
| Instituut/afd. | FNWI/FGw: Institute for Logic, Language and Computation (ILLC) |
| Trefwoorden | Provability Logic; Preservativity Logic; Heyting Arithmetic |
| Serie | ILLC Master of Logic Theses / ILLC ; MoL-2003-01 |
| Samenvatting | Some Intuitionistic Provability and Preservativity Logics (and their interrelations)
Chunlai Zhou
Abstract:
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. |
| Soort document | Preprint |
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