02-31
Formal Mathematical Systems including a Structural Induction Principle
by Kunik, M.
Preprint series: 02-31, Preprints
- MSC:
- 03F03 Proof theory, general
- 03B70 Logic of programming, See also {68Q55, 68Q60}
- 03D03 Thue and Post systems, etc.
- 03D05 Automata and formal grammars in connection with logical questions, See also {68Qxx}
Abstract: This study provides a general frame for formal mathematical systems which may be interesting for people working in formal logic, theoretical computer science and linguistics. We introduce recursive systems generating the recursively enumerable relations between lists of terms, the basic objects under consideration. A recursive system consists of axioms which are special quantifier-free positive horn formulas and of special rules of inference. Its extension to formal mathematical systems includes the predicate calculus as well as a structural induction principle with respect to the axioms of the underlying recursive system. We have also formulated our main results about formal mathematical systems for quite general restrictions in the argument lists of the formulas, which enables different kind of applications.
Keywords: Formal mathematical systems, structural induction principle, incompleteness theorems
Notes: This is a revised and extended version from March 26 (2003) which replaces the old version from September 22 (2002).
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