6533b82efe1ef96bd12926c1
RESEARCH PRODUCT
Derived sets and inductive inference
Kalvis Apsitissubject
Discrete mathematicsClass (set theory)Compact spaceRecursively enumerable languageLimit pointOrder (ring theory)IdentifiabilityInductive reasoningConstructiveMathematicsdescription
The paper deals with using topological concepts in studies of the Gold paradigm of inductive inference. They are — accumulation points, derived sets of order α (α — constructive ordinal) and compactness. Identifiability of a class U of total recursive functions with a bound α on the number of mindchanges implies \(U^{(\alpha + 1)} = \not 0\). This allows to construct counter-examples — recursively enumerable classes of functions showing the proper inclusion between identification types: EXα⊂EXα+1.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1994-01-01 |