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Punctual categoricity and a jump operation in the primitive recursive degrees
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The paper is devoted to the study of punctual structures such that any isomorphism between any of its punctual copies is primitive recursively reducible to a fixed 0, 1-valued oracle function. To estimate the complexity of such punctual structures and isomorphisms between them we introduce and investigate the weak (0, 1-valued) jump operation. In the paper we establish that there is a rigid punctual structure for which all isomorphisms are low under the weak jump, and at least one of them is not primitive recursive. Also we construct a rigid punctual structure with every isomorphism reducible to the weak jump of the zero function, and with at least one having a high degree.
Kazan Federal University
Title: Punctual categoricity and a jump operation in the primitive recursive degrees
Description:
The paper is devoted to the study of punctual structures such that any isomorphism between any of its punctual copies is primitive recursively reducible to a fixed 0, 1-valued oracle function.
To estimate the complexity of such punctual structures and isomorphisms between them we introduce and investigate the weak (0, 1-valued) jump operation.
In the paper we establish that there is a rigid punctual structure for which all isomorphisms are low under the weak jump, and at least one of them is not primitive recursive.
Also we construct a rigid punctual structure with every isomorphism reducible to the weak jump of the zero function, and with at least one having a high degree.
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