We examine a number of results of infinite combinatorics using the techniques of reverse mathematics. Our results are inspired by similar results in recursive combinatorics. Theor...
We define the weight of an integer N to be the smallest w such that N can be represented as w i=1 i2ci , with 1,..., w{1,-1}. Since arithmetic modulo a prime of low weight is parti...
We study the problem of proving in weak theories of Bounded Arithmetic the theorem that there are arbitrarily large prime numbers. We show that the theorem can be proved by some &...
Using appropriate notation systems for proofs, cutreduction can often be rendered feasible on these notations. Explicit bounds can be given. Developing a suitable notation system ...
This paper presents a new method – which does not rely on the cut-elimination theorem – for characterizing the provably total functions of certain intuitionistic subsystems of ...