Arnold Beckmann defined the uniform reduct of a propositional proof system f to be the set of those bounded arithmetical formulas whose propositional translations have polynomial size f-proofs. We prove that the uniform reduct of f + Extended Frege consists of all true bounded arithmetical formulas iff f + Extended Frege simulates every proof system.

We define the notion of the uniform reduct of a propositional proof system as the set of those bounded formulas in the language of Peano Arithmetic which have polynomial size proofs under the… Expand

The problem of the length of proofs of statements in finitely, axiomatized theory S is studied, in relation with problems of propositional proof systems.Expand