Abstract:
We show that each computably enumerable Turing degree is a degree of autostability relative to strong constructivizations for a decidable directed graph. We construct a decidable undirected graph whose autostability spectrum relative to strong constructivizations is equal to the set of all $PA$-degrees.
Keywords:computable model, strongly constructivizable model, autostability, autostability relative to strong constructivizations, degree of autostability relative to strong constructivizations, autostability spectrum relative to strong constructivizations, $PA$-degree, computably enumerable degree, graph.
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