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We sketch a constructive formal theory TCF of computable functionals, based on the partial continuous functionals as their intendend domain. Such a task had long ago been started by Dana Scott [12, 15], under the wellknown abbreviation LCF (logic of computable functionals). The present approach differs from Scott’s in two aspects. (i) The intended… (More)

- Basil A. Karádais
- Ann. Pure Appl. Logic
- 2016

We prove basic facts about the properties of atomicity and coherence for Scott information systems, and we establish direct connections between coherent information systems and well-known point-free structures.

• It is unlikely that there is an algorithm f that decides (1), i.e., returns tt if x = 0 and ff if x 6= 0: on input x = 0 it would run forever (think of the decimal representation of x); it would only semi-decide it, i.e., it would be a partial algorithm. • The algorithm as a mapping f : R→ B is discontinuous at 0. • Reals are Cauchy sequences of… (More)

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