On the strength of proof-irrelevant type theories
نویسندگان
چکیده
منابع مشابه
On the Strength of Proof-Irrelevant Type Theories
We present a type theory with some proof-irrelevance built into the conversion rule. We argue that this feature is useful when type theory is used as the logical formalism underlying a theorem prover. We also show a close relation with the subset types of the theory of PVS. We show that in these theories, because of the additional extentionality, the axiom of choice implies the decidability of ...
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Theories of proof-theoretic strength ψ(ΓΩ+1)
The purpose of this article is to present a range of theories with proof-theoretic ordinal ψ(ΓΩ+1). This ordinal parallels the ordinal of predicative analysis, Γ0, and our theories are parallel to classical theories of strength Γ0 such as ÎD<ω, FP0, ATR0, Σ1-DC0 + (SUB), and Σ1-AC0 + (SUB). We also relate these theories to the unfolding of ID1 which was already presented in the PhD thesis of th...
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ژورنال
عنوان ژورنال: Logical Methods in Computer Science
سال: 2008
ISSN: 1860-5974
DOI: 10.2168/lmcs-4(3:13)2008