Intermediate cumulation

In this snippet, I will describe a new case where overt wh-movement leads to additional scope possibilities

The Intermediate Higgs

Two paradigms for the origin of electroweak superconductivity are a weakly coupled scalar condensate, and a strongly coupled fermion condensate. The former suffers from a finetuning problem unless there are cancelations to radiative corrections, while the latter presents potential discrepancies with precision electroweak physics. Here we present a framework for electroweak symmetry breaking which interpolates between these two paradigms, and mitigates their faults. As in Little Higgs theories, the Higgs is a pseudo-Nambu Goldstone boson, potentially composite. The cutoff sensitivity of the one loop top quark contribution to the effective potential is canceled by contributions from additional vector-like quarks, and the cutoff can naturally be higher than in the minimal Standard Model. Unlike the Little Higgs models, the cutoff sensitivity from one loop gauge contributions is not canceled. However, such gauge contributions are naturally small as long as the cutoff is below 6 TeV. Precision electroweak corrections are suppressed relative to those of Technicolor or generic Little Higgs theories. In some versions of the intermediate scenario, the Higgs mass is computable in terms of the masses of these additional fermions and the Nambu-Goldstone Boson decay constant. In addition to the Higgs, new scalar and pseudoscalar particles are typically present at the weak scale

Normal intermediate subfactors

Let $N \subset M$ be an irreducible inclusion of type type II$_1$ factors with finite Jones index. We shall introduce the notion of normality for intermediate subfactors of the inclusion $N \subset M$. If the depth of $N \subset M$ is 2, then an intermediate subfactor $K$ for $N \subset M$ is normal in $N \subset M$ if and only if the depths of $N \subset K$ and $K \subset M$ are both 2. In particular, if $M$ is the crossed product $N \rtimes G$ of a finite group $G$, then $K = N \rtimes H$ is normal in $N \subset M$ if and only if $H$ is a normal subgroup of $G$.Comment: 25 pages, amslatex, to appear in J. Math. Soc. Japa

Topologies for intermediate logics

We investigate the problem of characterizing the classes of Grothendieck toposes whose internal logic satisfies a given assertion in the theory of Heyting algebras, and introduce natural analogues of the double negation and De Morgan topologies on an elementary topos for a wide class of intermediate logics.Comment: 21 page