On the number of \(L_{\infty\omega_1}\)-equivalent non-isomorphic models (Q2701681)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the number of \(L_{\infty\omega_1}\)-equivalent non-isomorphic models |
scientific article |
Statements
19 February 2001
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number of models
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ladder system
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uniformization
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infinitary logic
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iterated forcing
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colourings
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On the number of \(L_{\infty\omega_1}\)-equivalent non-isomorphic models (English)
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The authors show that it is consistent with ZFC+GCH that for every \(\kappa< \omega\) there is a model \(M\) of cardinality \(\omega_1\) which is \(L_{\infty \omega_1}\)-equivalent to exactly \(\kappa\) non-isomorphic models of cardinality \(\omega_1\). This is done by translating the problem into a purely combinatorial problem. So they work with colourings of ladder systems and show that for each prime \(p\) and positive integer \(m\) it is consistent with ZFC+GCH that there is a special ladder system having exactly \(p^m\) pairwise nonequivalent colourings.
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