Second order theories with ordinals and elementary comprehension (Q1908814)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Second order theories with ordinals and elementary comprehension |
scientific article; zbMATH DE number 851905
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Second order theories with ordinals and elementary comprehension |
scientific article; zbMATH DE number 851905 |
Statements
Second order theories with ordinals and elementary comprehension (English)
0 references
22 September 1996
0 references
We study elementary second-order extensions of the theory \(\text{ID}_1\) of noniterated inductive definitions and the theory \(\text{PA}_\Omega\) of Peano arithmetic with ordinals. We determine the exact proof-theoretic strength of those extensions and their natural subsystems, and we relate them to subsystems of analysis with arithmetic comprehension plus \(\Pi^1_1\) comprehension and bar induction without set parameters.
0 references
second-order arithmetic
0 references
elementary second-order extensions
0 references
inductive definitions
0 references
Peano arithmetic with ordinals
0 references
proof-theoretic strength
0 references
subsystems of analysis
0 references
arithmetic comprehension
0 references
bar induction
0 references
0 references
0 references
