Talk:Weakly compact cardinal: Difference between revisions
→"A relatively convoluted definition"
No edit summary |
|||
(One intermediate revision by the same user not shown) | |||
Line 4:
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
|