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Classical recursion theory

Piergiorgio Odifreddi
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TLDR
Theories of Recursive functions, Hierarchies of recursive functions, and Arithmetical sets: Recursively enumerable sets.
Abstract: 
Preface. Introduction. Theories of Recursive functions. Hierarchies of recursive functions. Recursively enumerable sets. Recursively enumerable degrees. Limit sets. Arithmetical sets. Arithmetical degrees. Enumeration degrees. Bibliography. Notation index. Subject index.

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The Medvedev lattice of computably closed sets

Sebastiaan A. Terwijn
- 01 Feb 2006 - 
TL;DR: A solution to a question of Simpson about Medvedev degrees of Π01 classes of positive measure that was independently solved by Simpson and Slaman is presented and the dual of does not allow an implication operator.
Journal ArticleDOI

Language learning from positive evidence, reconsidered: a simplicity-based approach.

Anne Hsu, +2 more
- 01 Jan 2013 - 
TL;DR: This study reviews recent formal results showing that the learner has sufficient data to learn successfully from positive evidence, if it favors the simplest encoding of the linguistic input.
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Selection Functions that Do Not Preserve Normality

Wolfgang Merkle, +1 more
- 01 Sep 2006 - 
TL;DR: It is shown that there are such languages that are only slightly more complicated than regular ones, namely, normality is preserved neither by deterministic one-counter languages nor by linear languages, and for both types of languages it is possible to select a constant sequence from a normal one.
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Index sets in computable analysis

Douglas Cenzer, +1 more
- 28 May 1999 - 
TL;DR: The notion of index sets associated with Π01 classes and with computably continuous functions is developed and the complexity of various problems of analysis is determined by the complexityof the associated index set.
Journal ArticleDOI

Noisy Inference and Oracles

Frank Stephan
TL;DR: It is shown that learning from a noisy informant is equal to finite learning with K-oracle from a usual informant and partial identification of all r.e. sets can cope also with noisy input.