by Kunik, M..

**Series:** 2002-31, Preprints

- MSC:
- 03F03 Proof theory, general
- 03B70 Logic in computer science
- 03D03 Thue and Post systems, etc.
- 03D05 Automata and formal grammars in connection with logical questions

**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 mathe\-matical 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