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Corpus ID: 201646387

Reflection algebras and conservation results for theories of iterated truth

@article{Beklemishev2019ReflectionAA,
title={Reflection algebras and conservation results for theories of iterated truth},
author={L. Beklemishev and F. Pakhomov},
journal={arXiv: Logic},
year={2019}
}

We consider extensions of the language of Peano arithmetic by transfinitely iterated truth definitions satisfying uniform Tarskian biconditionals. Without further axioms, such theories are known to be conservative extensions of the original system of arithmetic. Much stronger systems, however, are obtained by adding either induction axioms or reflection axioms on top of them. Theories of this kind can interpret some well-known predicatively reducible fragments of second-order arithmetic such as… CONTINUE READING