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Ordinal Computability: An Introduction to Infinitary Machines

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Ordinal Computability discusses models of computation obtained by generalizing classical models, such as Turing machines or register machines, to transfinite working time and space. In particular, recognizability, randomness, and applications to other areas of mathematics are covered.

Author(s): Merlin Carl
Series: De Gruyter Series in Logic and Its Applications 9
Publisher: de Gruyter
Year: 2019

Language: English
Pages: 343

Contents......Page 5
1. Introduction......Page 9
2. Machine models of transfinite computability......Page 17
3. Computability strength......Page 85
4. Recognizability......Page 165
5. Randomness......Page 203
6. Degree theory......Page 227
7. Complexity......Page 247
8. Applications and interactions......Page 265
9. Philosophical aspects......Page 285
Bibliography......Page 321
Index......Page 331