Transfinite type theory and provability of second order formulas
نویسندگان
چکیده
منابع مشابه
Kripke Models of Transfinite Provability Logic
For any ordinal Λ, we can define a polymodal logic GLPΛ, with a modality [ξ] for each ξ < Λ. These represent provability predicates of increasing strength. Although GLPΛ has no non-trivial Kripke frames, Ignatiev showed that indeed one can construct a universal Kripke frame for the variable-free fragment with natural number modalities, denoted GLPω. In this paper we show how to extend these con...
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چکیده ندارد.
Extending models of second order predicate logic to models of second order dependent type theory
We describe a method for constructing a model of second order dependent type theory out of a model of classical second order predicate logic. Apart from the construction being of interest by itself, this also suggests a way of proving the completeness of the formulas-as-types embedding from second order predicate logic to second order dependent type theory. Under this embedding, formulas are in...
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1977
ISSN: 0025-5645
DOI: 10.2969/jmsj/02940633