An Introduction to Inductive Definitions
Inductive definitions of sets are often informally presented by giving some rules for generating elements of the set and then adding that an object is to be in the set only if it has been generated according to the rules. An equivalent formulation is to characterize the set as the smallest set close...
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| Published in | Studies in Logic and the Foundations of Mathematics Vol. 90; pp. 739 - 782 |
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| Main Author | |
| Format | Book Chapter |
| Language | English |
| Published |
1982
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| Online Access | Get full text |
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| Summary: | Inductive definitions of sets are often informally presented by giving some rules for generating elements of the set and then adding that an object is to be in the set only if it has been generated according to the rules. An equivalent formulation is to characterize the set as the smallest set closed under the rules. This chapter discusses monotone induction and its role in extensions of recursion theory. The chapter reviews some of the work on non-monotone induction and outlines the separate motivation that has led to its development. The chapter briefly considers inductive definitions in a more general context. |
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| ISBN: | 9780444863881 0444863885 |
| ISSN: | 0049-237X |
| DOI: | 10.1016/S0049-237X(08)71120-0 |