02228nas a2200193 4500008004100000245004900041210004900090260003600139300001200175490000700187520164800194100002401842700001901866700002501885700001901910700003301929700002201962856005001984 2015 eng d00aUnfolding Feasible Arithmetic and Weak Truth0 aUnfolding Feasible Arithmetic and Weak Truth aDordrechtbSpringer Netherlands a153-1670 v363 aIn this paper we continue Feferman?s unfolding program initiated in (Feferman, vol. 6 of Lecture Notes in Logic, 1996) which uses the concept of the unfolding U(S) of a schematic system S in order to describe those operations, predicates and principles concerning them, which are implicit in the acceptance of S. The program has been carried through for a schematic system of non-finitist arithmetic NFA in Feferman and Strahm (Ann Pure Appl Log, 104(1?3):75?96, 2000) and for a system FA (with and without Bar rule) in Feferman and Strahm (Rev Symb Log, 3(4):665?689, 2010). The present contribution elucidates the concept of unfolding for a basic schematic system FEA of feasible arithmetic. Apart from the operational unfolding U0(FEA) of FEA, we study two full unfolding notions, namely the predicate unfolding U(FEA) and a more general truth unfolding UT(FEA) of FEA, the latter making use of a truth predicate added to the language of the operational unfolding. The main results obtained are that the provably convergent functions on binary words for all three unfolding systems are precisely those being computable in polynomial time. The upper bound computations make essential use of a specific theory of truth TPT over combinatory logic, which has recently been introduced in Eberhard and Strahm (Bull Symb Log, 18(3):474?475, 2012) and Eberhard (A feasible theory of truth over combinatory logic, 2014) and whose involved proof-theoretic analysis is due to Eberhard (A feasible theory of truth over combinatory logic, 2014). The results of this paper were first announced in (Eberhard and Strahm, Bull Symb Log 18(3):474?475, 2012).1 aEberhard, Sebastian1 aStrahm, Thomas1 aAchourioti, Theodora1 aGalinon, Henri1 aFernández, José, Martínez1 aFujimoto, Kentaro uhttp://www.iam.unibe.ch/ltgpub/2015/esu15.pdf