Description: The monadic theory \(MT(\omega_{1},<)\) mentioned in Form 246 is defined
Content:
The monadic theory \(MT(\omega_{1},<)\) mentioned in Form 246 is defined as follows: The language has a countable set \(x, y,\ldots\) of variables ranging over \(\omega_{1}\), a countable set of variables \(X, Y,\ldots\) ranging over subsets of \(\omega_{1}\), a relation \( \le \) on \(\omega _{1}\) and a relation \(\in\) between individual variables and set variables. The formulas are built up with the usual logical connectives and quantifiers \(\forall\) and \(\exists \) on both types of variables. \(MT(\omega _{1}, \le)\) is the set of all sentences true in \((\omega _{1}, \le)\)
Howard-Rubin number: 85
Type: Definition
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