Computability over the partial continuous functionals
نویسندگان
چکیده
منابع مشابه
Computability over The Partial Continuous Functionals
We show that to every recursive total continuous functional Φ there is a representative Ψ of Φ in the hierearchy of partial continuous functionals such that Ψ is S1 − S9 computable over the hierarchy of partial continuous functionals. Equivalently, the representative Ψ will be PCF -definable over the partial continuous functionals, where PCF is Plotkin’s programming language for computable func...
متن کاملRecursion on the partial continuous functionals
We describe a constructive theory of computable functionals, based on the partial continuous functionals as their intendend domain. Such a task had long ago been started by Dana Scott [28], under the well-known abbreviation LCF. However, the prime example of such a theory, Per Martin-Löf’s type theory [24] in its present form deals with total (structural recursive) functionals only. An early at...
متن کاملThe continuous functionals of finite types over the reals
We investigate a hierarchy of domains with totality where we close some selected base domains, including domains for the reals, the natural numbers and the boolean values, under cartesian products and restricted function spaces. We show that the total objects will be dense in the respective domains, and that our construction is equivalent to the analogue construction in the category of limit sp...
متن کاملContinuous Functions over Discrete Partial Orders
This paper examines the properties of structure preserving morphisms f over discrete partial orders. It employs concepts of continuity and path homomorphisms. It will conclude that no single constraint on f will be sufficient, and it will also conclude that a convexity constraint on f−1 seems to be essential. We employ closure lattices to help reach this conclusion.
متن کاملBanach Algebra of Continuous Functionals and the Space of Real-Valued Continuous Functionals with Bounded Support
In this article, we give a definition of a functional space which is constructed from all continuous functions defined on a compact topological space. We prove that this functional space is a Banach algebra. Next, we give a definition of a function space which is constructed from all real-valued continuous functions with bounded support. We prove that this function space is a real normed space.
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: 2000
ISSN: 0022-4812,1943-5886
DOI: 10.2307/2586691