Realization of analysis into Explicit Mathematics
نویسندگان
چکیده
منابع مشابه
Realization of Analysis into Explicit Mathematics
We define a novel interpretation R of second order arithmetic into Explicit Mathematics. As a difference from standard D-interpretation, which was used before and was shown to interpret only subsystems proof-theoretically weaker than T0, our interpretation can reach the full strength of T0. The R-interpretation is an adaptation of Kleene’s recursive realizability, and is applicable only to intu...
متن کاملRealization of constructive set theory into explicit mathematics: a lower bound for impredicative Mahlo universe
We define a realizability interpretation of Aczel’s Constructive Set Theory CZF into Explicit Mathematics. The final results are that CZF extended by Mahlo principles is realizable in corresponding extensions of T0, thus providing relative lower bounds for the proof-theoretic strength of the latter.
متن کاملFirst steps into metapredicativity in explicit mathematics
Metapredicativity is a new general term in proof theory which describes the analysis and study of formal systems whose proof-theoretic strength is beyond the Feferman-Schütte ordinal Γ0 but which are nevertheless amenable to purely predicative methods. Typical examples of formal systems which are apt for scaling the initial part of metapredicativity are the transfinitely iterated fixed point th...
متن کاملUniverses in explicit mathematics
This paper deals with universes in explicit mathematics. After introducing some basic definitions, the limit axiom and possible ordering principles for universes are discussed. Later, we turn to least universes, strictness and name induction. Special emphasis is put on theories for explicit mathematics with universes which are proof-theoretically equivalent to Feferman’s T0.
متن کاملImpredicative Overloading in Explicit Mathematics
We introduce the system OTN of explicit mathematics based on elementary separation, products, joins and weak power types. In this theory, we will define late-bound overloaded functions with a corresponding impredicative type structure à la λ&. Then we present a set-theoretic model for OTN which provides a denotational semantics for impredicative overloading without restricting itself to early-b...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2001
ISSN: 0022-4812,1943-5886
DOI: 10.2307/2694980