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- Andrej Bauer, Dana S. Scott, Steven M. Awodey, Lenore Blum, Abbas Edalat, Frank Pfenning +51 others
- 2000

An approach for a simple, general, and unified theory of effectivity on sets with cardinality not greater than that of the continuum is presented. A standard theory of effectivity on F = {f : N 3 N} has been developed in a previous paper. By representations 6: B-* M this theory is extended to other sets M. Topological and recursion theoretical properties of… (More)

Scientists apply digital computers to perform computations on natural numbers, nite strings, real numbers and more general objects like sets, functions and measures. While computability theory on many countable sets is well established and for computability on the real numbers several (unfortunately mutually non-equivalent) deenitions are being studied, in… (More)

Although numerous computer programs have been written to compute sets of points which claim to approximate Julia sets, no reliable high precision pictures of non-trivial Julia sets are currently known. Usually, no error estimates are added and even those algorithms which work reliably in theory, become unreliable in practice due to rounding errors and the… (More)

In the representation approach to computable analysis (TTE) [Grz55, KW85, Wei00], abstract data like rational numbers, real numbers, compact sets or continuous real functions are represented by finite or infinite sequences (Σ * , Σ ω) of symbols, which serve as concrete names. A function on abstract data is called computable , if it can be realized by a… (More)