Realizability, Set Theory and Term Extraction
نویسندگان
چکیده
3 Recursive Realizability Interpretations 16 3.1 Abstract Applicative Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.2 Realizability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.3 Soundness for IZF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.4 Term Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.5 Strong Intuitionistic Counterexamples . . . . . . . . . . . . . . . . . . . . . . . . 24 3.6 Some famous “nonstandard” consistency results . . . . . . . . . . . . . . . . . . . 25
منابع مشابه
Kripke Semantics for Dependent Type Theory and Realizability Interpretations
Constructive reasoning has played an increasingly important role in the development of provably correct software. Both typed and type-free frameworks stemming from ideas of Heyting, Kleene, and Curry have been developed for extracting computations from constructive specifications. These include Realizability, and Theories based on the Curry-Howard isomorphism. Realizability – in its various typ...
متن کاملExtracting Programs from Constructive HOL Proofs Via IZF Set-Theoretic Semantics
Church’s Higher Order Logic is a basis for proof assistants — HOL and PVS. Church’s logic has a simple set-theoretic semantics, making it trustworthy and extensible. We factor HOL into a constructive core plus axioms of excluded middle and choice. We similarly factor standard set theory, ZFC, into a constructive core, IZF, and axioms of excluded middle and choice. Then we provide the standard s...
متن کاملLifschitz realizability for intuitionistic Zermelo-Fraenkel set theory
A variant of realizability for Heyting arithmetic which validates Church’s thesis with uniqueness condition, but not the general form of Church’s thesis, was introduced by V. Lifschitz in [15]. A Lifschitz counterpart to Kleene’s realizability for functions (in Baire space) was developed by van Oosten [19]. In that paper he also extended Lifschitz’ realizability to second order arithmetic. The ...
متن کاملKrivine's classical realisability from a categorical perspective
In a sequence of papers (Krivine 2001; Krivine 2003; Krivine 2009) J.-L. Krivine has introduced his notion of Classical Realizability for classical second order logic and Zermelo-Fraenkel set theory. Moreover, in more recent work (Krivine 2008) he has considered forcing constructions on top of it with the ultimate aim of providing a realizability interpretation for the axiom of choice. The aim ...
متن کاملRealizability algebras III: some examples
The notion of realizability algebra, which was introduced in [17, 18], is a tool to study the proof-program correspondence and to build new models of set theory, which we call realizability models of ZF. It is a variant of the well known notion of combinatory algebra, with a new instruction cc, and a new type for the environments. The sets of forcing conditions, in common use in set theory, are...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007