A new conservation result of \(\text{WKL}_0\) over \(\text{RCA}_0\) (Q1407524)
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scientific article; zbMATH DE number 1982460
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A new conservation result of \(\text{WKL}_0\) over \(\text{RCA}_0\) |
scientific article; zbMATH DE number 1982460 |
Statements
A new conservation result of \(\text{WKL}_0\) over \(\text{RCA}_0\) (English)
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16 September 2003
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The conservation result of the title shows that if WKL\(_0\) proves a sentence of the form \[ (\forall X)(\exists ! Y) \psi (X,Y) \] where \(\psi\) is a \(\Sigma^0_3\)-formula, then RCA\(_0\) also proves the sentence. This result is extended to all arithmetical formulas \(\psi\) in the article of \textit{S. G. Simpson}, \textit{K. Tanaka}, and \textit{T. Yamazaki} [Ann. Pure Appl. Logic 118, 87-114 (2002; Zbl 1016.03064)].
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reverse mathematics
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conservation
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WKL
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forcing
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