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Abstract. We classify and compare recursive and iterative definitions of total computable functions according to the complexity of the ordinal structures needed ...
We classify and compare recursive and iterative definitions of total computable functions according to the complexity of the ordinal structures needed to ...
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Let us see how Hardy computations are mimicked under this encoding of ordinals. The tail recursive definitions of the Hardy hierarchy can be seen as the ...
Oct 18, 2020 · From what I understand, an ordinal α is recursive if it is the order type of a subset of N that is well-ordered by a recursive relation ≺ ( ...
Jul 30, 2008 · In chapter two new notions of elementary and primitive recursive ordinals are given, in the context of the material developed on tree-ordinals.
Ordinal arithmetic provides foundational tools for discussing transfinite induction and recursion, linking it closely to recursive definitions and structures.
Abstract. Data Nets are a version of colored Petri nets in which tokens carry data taken from an infinite, linearly ordered and dense domain.
Recursive ordinals are closely related to the concept of computability, as they mark the boundaries within which recursive functions can be effectively defined.
May 23, 2022 · An ordinal analysis of a formal system precisely measures its proof-theoretic strength, which is its strength at justifying transfinite ...