Talk:Weakly compact cardinal: Difference between revisions
→"A relatively convoluted definition"
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Then there is only one major change between the compactness theorem and the weak compactness property:
* When \(\Gamma\) is a set of \(\mathcal L_{\omega,\omega}\)-sentences <u>of size \(\underline{<\aleph_0}\)</u>, if every subset of \(\Gamma\) of size \(<\aleph_0\) has a model, then \(\Gamma\) has a model.
* When \(\Gamma\) is a set of \(\mathcal L_{\kappa,\kappa}\)-sentences of size \(<\kappa\), if every subset of \(\Gamma\) of size \(<\kappa\) has a model, then \(\Gamma\) has a model.
where the change is the
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