Description:
Some relationships between forms 271(\(n\)) and 45(\(n\)) are given
Content:
In Kolany/Wojtylak [1991] some relationships between forms 271(\(n\)) and 45(\(n\)) are given. Form 271(\(n\)) is \(CT_{n}\): The compactness theorem for the propositional calculus restricted to sets of formulas where each variable occurs in at most \(n\) formulas, and Form 45(\(n\)) is \(C(\infty,n).)\) For example, \(CT_{m}\) implies \(C(\infty ,n)\) if \(m \ge n! + n(n - 1)\). Also considered are forms \(CT^{*}_{m}\) (\(CT_{m}\) restricted to formulas which are disjunctions of formulas of the form \(p\) or \((\neg p)\) where \(p\) is a propositional variable). For example, it is shown that \(CT^*_3\) implies \(C(\infty,2)\).
Howard-Rubin number: 92
Type: Relationships
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