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math.LO2010★ 2 cited
Separating Bounded Arithmetics by Herbrand Consistency
Saeed Salehi
The problem of separating the hierarchy of bounded arithmetic has been studied in the paper. It is shown that the notion of Herbrand Consistency, in its full generality, cann…
math.LO2010★ 5 cited
Herbrand Consistency of Some Arithmetical Theories
Saeed Salehi
Gödel's second incompleteness theorem is proved for Herbrand consistency of some arithmetical theories with bounded induction, by using a technique of logarithmic shrinking the wit…