The Kolmogorov–Arnold representation theorem revisited

The Separatrix Theorem Revisited

We present a simple proof of Camacho-Sad’s Theorem on the existence of invariant analytic curves for singular holomorphic foliations in (C2, 0), avoiding the combinatorial arguments on the residues by means of a ramification.

The PCF Theorem Revisited

i<κ λi/I, where κ < mini<κ λi. Here we prove this theorem under weaker assumptions such as wsat(I) < mini<κ λi, where wsat(I) is the minimal θ such that κ cannot be delivered to θ sets / ∈ I (or even slightly weaker condition). We also look at the existence of exact upper bounds relative to <I (<I −eub) as well as cardinalities of reduced products and the cardinals TD(λ). Finally we apply this ...

The folk theorem revisited !

This paper develops a simple “instant-response” model of strategic behavior where players can react instantly to changing circumstances, but at the same time face some inertia after changing action. The framework is used to reconsider the folk theorem and, in particular, the role of the key condition of dimensionality. In contrast to the discounted case in discrete time, here low dimensionality...

The Conservation Theorem revisited

This paper describes a method of proving strong normalization based on an extension of the conservation theorem. We introduce a structural notion of reduction that we call βS , and we prove that any λ-term that has a βIβS-normal form is strongly β-normalizable. We show how to use this result to prove the strong normalization of different typed λ-calculi.

The Wulff theorem revisited