Minimal model of \(''\aleph ^ L_ 1\) is countable'' and definable reals (Q1820156)
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scientific article; zbMATH DE number 3993576
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Minimal model of \(''\aleph ^ L_ 1\) is countable'' and definable reals |
scientific article; zbMATH DE number 3993576 |
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Minimal model of \(''\aleph ^ L_ 1\) is countable'' and definable reals (English)
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1985
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First, a result of Prikry is proved, namely, if M is a countable, transitive model of \(ZFC+V=L\), then there is a generic extension which is a minimal model of \(''\omega^ L_ 1\) is countable''. In the second part this construction is modified to get a generic extension M[a], \(a\leq \omega\), with M[a] still a minimal model of \(''\omega^ L_ 1\) is countable'', and such that a is a \(\Pi^ 1_ 2\) singleton and all constructible reals are recursive in a.
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minimal collapse
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minimal model
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generic extension
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