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arithmetical hierarchy (Definition)
ArithmeticalHierarchy

"arithmetical hierarchy" is owned by CWoo. [ full author list (4) | owner history (3) ]
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See Also: analytic hierarchy

Other names:  arithmetic hierarchy, arithmetic, arithmetical, arithmetic formula, arithmetical formulas
Also defines:  sigma n, sigma-n, pi n, pi-n, delta n, delta-n, recursive, recursively enumerable, delta-0, delta 0, delta-1, delta 1, arithmetical

Attachments:
arithmetical hierarchy is a proper hierarchy (Result) by Henry
$\Delta_1$ bootstrapping (Example) by Henry
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Cross-references: graph, functions, analytic hierarchy, necessary, superscript, integer, classes, complements, negation, computer, primitive recursive, quantifiers, bounded, level, relations, formulas
There are 69 references to this entry.

This is version 16 of arithmetical hierarchy, born on 2002-08-06, modified 2008-07-10.
Object id is 3272, canonical name is ArithmeticalHierarchy.
Accessed 34334 times total.

Classification:
AMS MSC03B10 (Mathematical logic and foundations :: General logic :: Classical first-order logic)

Pending Errata and Addenda
None.
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Discussion
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Pi^0_n definition correct? by iddo on 2003-09-02 06:20:19
I think that $Pi^0_n$ definition should require that $xi$ (the inner formula) be a $Delta_0$ formula, and not $Delta^0_1$.
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