A theory of truth is introduced for a first--order language L of set theory. Fully interpreted metalanguages which contain their truth predicates are constructed for L. The presented theory is free from infinite regress, whence it provides a proper framework to study the regress problem. Only ZF set theory, concepts definable in L and classical two-valued logic are used.
Keywords truth theory  language of set theory  metalanguage  fixed point  regress problem  transfinite regress
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Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Human Knowledge and the Infinite Regress of Reasons.Peter D. Klein - 1999 - Philosophical Perspectives 13:297-325.
Axiomatic Theories of Truth.Volker Halbach - 2008 - Stanford Encyclopedia of Philosophy.

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