An uncountable cardinal $\kappa$ is a <strongly compact cardinal> when every $\kappa$-satisfiable theory in any $L_{\kappa,\kappa}$ language is satisfiable. Unlike weak compactness, there is no cardinality bound on the language.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 116 / 1 / a / iv / Solution

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