At first sight, the argument which F. P. Ramsey gave for (the infinite case of) his famous theorem from 1927, is hopelessly unconstructive. If suitably reformulated, the theorem is true intuitionistically as well as classically: we offer a proof which should convince both the classical and the intuitionistic reader.

Let G be a simple connected graph with n vertices and m edges and let d(e1) > d(e2) > · · · > d(em) be edge degree sequence of graph G. Denote by EF = ∑m i=1 d(ei) 3 reformulated forgotten index of G. Lower and upper bounds for the invariant EF are obtained.

This paper discusses some serious difficulties for what we shall call the standard account of various kinds of relative necessity, according to which any given kind of relative necessity may be defined by a strict conditional necessarily, if C then p where C is a suitable constant proposition, such as a conjunction of physical laws. We argue, with the help of Humberstone (Reports on Mathematica...

We point out a connection between reflection principles and generic large cardinals. One principle of pure reflection is introduced that is as strong as generic supercompactness of ω2 by σ-closed forcing. This new concept implies CH and extends the reflection principles for stationary sets in a canonical way.

The HOMA (Harmonic Oscillator Model of Aromaticity) index, reformulated in 1993, has been very often applied to describe π-electron delocalization for monoand polycyclic π-electron systems. However, different measures of π-electron delocalization were employed for the CC, CX, and XY bonds, and this index seems to be inappropriate for compounds containing heteroatoms. In order to describe proper...