In 1984, Henson and Rubel proved the following theorem: If p(x1, ..., xn) is an exponential polynomial with coefficients in C with no zeroes in C, then p(x1, ..., xn) = e g(x1,...,xn) for some exponential polynomial g(x1, ..., xn) over C. In this paper, I will prove the analog of this theorem for Zilber’s Pseudoexponentiation directly from the axioms. Furthermore, this proof relies only on the ...

We prove that, if a mild condition on the hyperbolicity of the periodic points holds for any diffeomorphism in a residual subset of a C-open set U , then such set U exhibits a residual subset A of Axiom A diffeomorphisms. We also prove an analogous result for nonsingular endomorphisms: if a mild expanding condition holds for the periodic set of local diffeomorphisms belonging in a residual subs...

We approach the recognition of textual entailment using logical semantic representations and a theorem prover. In this setup, lexical divergences that preserve semantic entailment between the source and target texts need to be explicitly stated. However, recognising subsentential semantic relations is not trivial. We address this problem by monitoring the proof of the theorem and detecting unpr...

We present a new development in our approach to the covariant quantization of superstrings in 10 dimensions which is based on a gauged WZNW model. To incorporate worldsheet diffeomorphisms we need the quartet of ghosts (bzz, c , βzz, γ ) for topological gravity. The currents of this combined system form an N = 2 superconformal algebra. The model has vanishing central charge and contains two ant...

We consider an Axiom A diffeomorphism and the invariant set of orbits which never falls into a fixed hole. We study various aspects of the complexity of the symbolic representation of Ω. Our main result are that each topologically transitive component of Ω is coded and that typically Ω is of finite type.

In this paper I will communicate some new consequences of the Proper Forcing Axiom. First, the Bounded Proper Forcing Axiom implies that there is a well ordering of R which is Σ1-definable in (H(ω2),∈). Second, the Proper Forcing Axiom implies that the class of uncountable linear orders has a five element basis. The elements are X, ω1, ω∗ 1 , C, C ∗ where X is any suborder of the reals of size ...

[W]e require certain indemonstrable propositions, which hitherto I have not succeeded in reducing to less than ten. Some indemonstrables there must be; and some propositions, such as the syllogism, must be of the number, since no demonstration is possible without them. But concerning others, it may be doubted whether they are indemonstrable or merely undemonstrated; and it should be observed th...

The AGM postulates [4], [1] are widely regarded to have captured much of what is involved in the process of rational belief revision. Recently however, Parikh [7] observed that despite their success, the AGM postulates are rather liberal in their treatment of the notion of relevance. More precisely, Parikh argues that during belief revision a rational agent does not change her entire belief cor...

Consider the family of Schrödinger operators (and also its Dirac version) on l(Z) or l(N) H W ω,S = ∆+ λF (S n ω) +W, ω ∈ Ω, where S is a transformation on (compact metric) Ω, F a real Lipschitz function and W a (sufficiently fast) power-decaying perturbation. Under certain conditions it is shown that H ω,S presents quasi-ballistic dynamics for ω in a dense Gδ set. Applications include potentia...