Unfolding Feasible Arithmetic and Weak Truth

In 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).

Standard cystectomy fits all: truth or myth?

Radical cystectomy (RC) with pelvic lymph node dissection (PLND) followed by urinary diversion is the treatment of choice for muscle-invasive bladder cancer (BC) and non-invasive BC refractory to transurethral resection of the bladder (TUR-B) and/or intravesical instillation therapies. Since the morbidity and possible mortality of this surgery are relevant, care must be taken in the preoperative selection of patients for the various organ-sparing procedures (e.g., bladder-sparing, nerve sparing, seminal vesicle sparing) and various types of urinary diversion. The patient’s performance status and comorbidities, along with individual tumor characteristics, determine possible surgical steps during RC. This individualized approach to RC in each patient can maximize oncological safety and minimize avoidable side effects, rendering ‘standard’ cystectomy a surgery of the past.