  In this paper a class of languages which are formal enough for mathematical
reasoning is introduced. First-order formal languages containing natural
numbers and numerals belong to that class. Its languages are called
mathematically agreeable (shortly MA). Languages containing a given MA language
L, and being sublanguages of L augmended by a monadic predicate are
constructed. A mathematical theory of truth (shortly MTT) is formulated for
some of these languages. MTT makes them MA languages which posses their own
truth predicates. MTT is shown to conform well with the eight norms presented
for theories of truth in 'What Theories of Truth Should be Like (but Cannot
be)', by Hannes Leitgeb. MTT is free from infinite regress, providing a proper
framework to study the regress problem. Main tools used in proofs are
Zermelo-Fraenkel (ZF) set theory and classical logic.
