A \(\Pi_ 2^ 1\) singleton incompatible with \(0^ \#\) (Q1315458)
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scientific article; zbMATH DE number 513340
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A \(\Pi_ 2^ 1\) singleton incompatible with \(0^ \#\) |
scientific article; zbMATH DE number 513340 |
Statements
A \(\Pi_ 2^ 1\) singleton incompatible with \(0^ \#\) (English)
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10 March 1994
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It is shown that there is a \(\Pi_ 2^ 1\) formula \(\Phi\) of second- order number theory such that if at most one real can satisfy \(\Phi\) in any model of ZF, if \(V=L\), then no real satisfies it, and it is consistent that some \(b\) satisfies it and \(L\) and \(L[b]\) have the same cardinals. The latter consistency is via a class forcing over the minimal model of ZF. The result is motivated by Solovay's conjecture on \(\Pi_ 2^ 1\) reals.
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0 sharp
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consistency
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class forcing
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Solovay's conjecture
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\(\Pi_ 2^ 1\) reals
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