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1. • CommentRowNumber1.
   • CommentAuthorzskoda
   • CommentTimeNov 2nd 2022
   • PermaLink
   Author: zskoda
   Format: MarkdownItexA topic in predicate logic. <a href="https://ncatlab.org/nlab/revision/rule+C/1">v1</a>, <a href="https://ncatlab.org/nlab/show/rule+C">current</a>

   A topic in predicate logic.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorRodMcGuire
   • CommentTimeNov 3rd 2022
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   Author: RodMcGuire
   Format: MarkdownItexIsn't this just a Skolem constant, a Skolem function of 0 arguments where an existential variable is replaced by a newly created function that gives a value for it? [https://en.wikipedia.org/wiki/Skolem_normal_form](https://en.wikipedia.org/wiki/Skolem_normal_form) [https://encyclopediaofmath.org/index.php?title=Skolem_function](https://encyclopediaofmath.org/index.php?title=Skolem_function) says they were introduced by Skolem in the 1920s

   Isn’t this just a Skolem constant, a Skolem function of 0 arguments where an existential variable is replaced by a newly created function that gives a value for it?

   https://en.wikipedia.org/wiki/Skolem_normal_form

   https://encyclopediaofmath.org/index.php?title=Skolem_function

   says they were introduced by Skolem in the 1920s

3. • CommentRowNumber3.
   • CommentAuthorzskoda
   • CommentTimeNov 3rd 2022
   • (edited Nov 3rd 2022)
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   Author: zskoda
   Format: MarkdownItexThe idea is essentially the same, but it is not the same thing. Skolemization is a procedure in model theory, _replacing_ a sentence with equisatisfiable sentence without one existential quantifier, and also a theory with a Skolem theory. Rule C is a notion in _proof theory_, adding a rule of inference (in generalized sense), which is not in pure predicate logic, as a temporary tool, with a basic theorem saying that if a sentence not involving the temporary variable is provable with rule C then it is provable in pure predicate logic as well. As far as who first formalized proof theoretic rule C, Mendelson asserts that it is _likely_ from Rosser, and Mendelson was quite an authority (and certainly quite familiar with Skolemization).

   The idea is essentially the same, but it is not the same thing. Skolemization is a procedure in model theory, replacing a sentence with equisatisfiable sentence without one existential quantifier, and also a theory with a Skolem theory. Rule C is a notion in proof theory, adding a rule of inference (in generalized sense), which is not in pure predicate logic, as a temporary tool, with a basic theorem saying that if a sentence not involving the temporary variable is provable with rule C then it is provable in pure predicate logic as well.

   As far as who first formalized proof theoretic rule C, Mendelson asserts that it is likely from Rosser, and Mendelson was quite an authority (and certainly quite familiar with Skolemization).