Comments on two theorems by Kandel

Eric Kandel

Comments on Some Completeness Theorems of Urquhart and Méndez & Salto

Urquhart [8] and Méndez & Salto [5, 6] claim to establish completeness theorems for the system C and two of its negation extensions. In this note, we do the following three things: (1) provide a counterexample to all of these alleged completeness theorems, (2) attempt to diagnose the mistakes in the reported completeness proofs, and (3) provide complete axiomatizations of the desired systems.

Comments on No-hair Theorems and Stabilty of Blackholes

In the light of recent blackhole solutions inspired by string theory, we review some old statements on field theoretic hair on blackholes. We also discuss some stability issues. In particular we argue that the two dimensional string blackhole solution is semi-classically stable while the naked singularity is unstable to tachyon fluctuations. Finally we comment on the relation between the linear...

Two theorems on experimental logics

A generalization of a formal system is considered, in which the axioms of the formal system can be withdrawn or supplemented, as mechanical experimentation proceeds through time and the consequences of various combinations of assumptions are realized. The "theorems" of these experimental logics are taken to be those assertions possessing a proof which remains valid for all "sufficiently large t...

Two Theorems on Galois Cohomology1

Notice that we have dropped the hypothesis that both k and K be Galois over the rationals. To see how Theorem 1 generalizes Yokoi's result, remember that if G has prime order p, then multiplication by p annihilates all the cohomology groups. Thus in this case the cohomology groups are determined up to isomorphism by their order. The technique used to prove Theorem 1 can be used to prove other r...