Form equivalence class Howard-Rubin Number: 43
Statement: Countable Henkin Principle: Let \(\Phi\) be theclass of formulas in a language that includes the language of thesentential calculus. Let \(I\) be a countable set of inferences, and\(\Gamma\) a consistent subset of \(\Phi\) such that \(\Gamma\cup\{\psi\}\)respects \(I\) for each \(\psi\in\Phi\). Then for any \(\phi\in\Phi\), if\(\phi\) is consistent with \(\Gamma\) then \(\Gamma\) has a finitelyconsistent extension that contains \(\phi\) and decides \(I\). Goldblatt [1985] and Note 126.
Howard-Rubin number: 43 B
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