Related papers: Few non-minimal types and non-structure
We introduce and study diamonds of GL(2,R)-invariant subvarieties of Abelian and quadratic differentials, which allow us to recover information on an invariant subvariety by simultaneously considering two degenerations, and which provide a…
Borrowing some terminology from pro-p groups, thin Lie algebras are N-graded Lie algebras of width two and obliquity zero, generated in degree one. In particular, their homogeneous components have degree one or two, and they are termed…
We prove that for any two minimal models of an lc algebraically integrable foliated triple on potentially klt varieties, there exist small birational models that are connected by a sequence of flops. In particular, any two minimal models of…
A natural construction of the logarithmic extension of the M(2,p) minimal models is presented, which generalises our previous model [0708.0802] of percolation (p=3). Its key aspect is the replacement of the minimal model irreducible modules…
We introduce a simple extension of the $\lambda$-calculus with pairs---called the distributive $\lambda$-calculus---obtained by adding a computational interpretation of the valid distributivity isomorphism $A \Rightarrow (B\wedge C)\ \…
Given a $k$-graph $\Lambda$ and an element $p$ of $\NN^k$, we define the dual $k$-graph, $p\Lambda$. We show that when $\Lambda$ is row-finite and has no sources, the $C^*$-algebras $C^*(\Lambda)$ and $C^*(p\Lambda)$ coincide. We use this…
We prove several structural results on Nottingham algebras, a class of infinite-dimensional, modular, graded Lie algebras, which includes the graded Lie algebra associated to the Nottingham group with respect to its lower central series.…
A longstanding open problem in lambda calculus is whether there exist continuous models of the untyped lambda calculus whose theory is exactly the least lambda-theory lambda-beta or the least sensible lambda-theory H (generated by equating…
We prove the existence of weak integral canonical models of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic $(0,p)$. As a first application we solve a conjecture of Langlands for Shimura varieties of Hodge type.…
For symmetric Kashiwara crystals of type $A$ and rank $e=2$, and for the canonical basis elements that we call external, corresponding to weights on the outer skin of the Kashiwara crystal, we construct the canonical basis elements in a…
We investigate the complexity of modal satisfiability for certain combinations of modal logics. In particular we examine four examples of multimodal logics with dependencies and demonstrate that even if we restrict our inputs to…
In this note we study the weak topology on paired modules over a (not necessarily commutative) ground ring. Over QF rings we are able to recover most of the well known properties of this topology in the case of commutative base fields. The…
Consider an a.e.c. (abstract elementary class), that is, a class K of models with a partial order refining inclusion (submodel) which satisfy the most basic properties of an elementary class. Our test question is trying to show that the…
Suppose that lambda = mu^+. We consider two aspects of the square property on subsets of lambda. First, we have results which show e.g. that for aleph_0 <= kappa =cf (kappa)< mu, the equality cf([mu]^{<= kappa}, subseteq)= mu is a…
It is well-known that the square principle $\square_\lambda$ entails the existence of a non-reflecting stationary subset of $\lambda^+$, whereas the weak square principle $\square^*_\lambda$ does not. Here we show that if…
Let $A$ be an integral $k$-algebra of finite type over a field $k$ of characteristic zero. Let ${\cal{F}}$ be a family of $k$-derivations on $A$ and $M_{\cal{F}}$ the $A$-module spanned by ${\cal{F}}$. In this paper, we generalize a result…
The decidability of axiomatic extensions of the modal logic K with modal reduction principles, i.e. axioms of the form $\Diamond^{k} p \rightarrow \Diamond^{n} p$, has remained a long-standing open problem. In this paper, we make…
In this letter I discuss a class of extensions of the standard model that have a minimal number of possible parameters, but can in principle explain dark matter and inflation. It is pointed out that the so-called new minimal standard model…
We introduce a new notion called generalized dominated splitting which is weaker than classical dominated splitting. We use this notion to generalize a result of Zhang\cite{Zh}: every diffeomorphism with nontrivial global generalized…
We investigate the class of models of a general dependent theory. We continue math.LO/0702292 in particular investigating so called "decomposition of types"; thesis is that what holds for stable theory and for Th(Q,<) hold for dependent…