Polynomial–time constant–space quantum Turing machines (QTMs) and logarithmic–space probabilistic Turing machines (PTMs) recognize uncountably many languages with bounded error (Say and Yakaryılmaz 2014, arXiv:1411.7647). In this paper, we investigate more restricted cases for both models to recognize uncountably many languages with bounded error. We show that double logarithmic space is enough...

In this paper, we create many examples of hyperbolic groups with subgroups satisfying interesting finiteness properties.We give the first which are type $FP_2$ but not finitely presented. We uncountably similar properties to those groups. Along way more presented $FP_3$.

Abstract We prove a multivariate Lagrange-Good formula for functionals of uncountably many variables and investigate its relation with inversion formulas using trees. clarify the cancellations that take place between two aforementioned draw connections similar approaches in range applications.

We consider the equation 1 $$\begin{aligned} \Delta _x u+u_{yy}+f(u)=0,\quad x=(x_1,\dots ,x_N)\in {{\mathbb {R}}}^N,\ y\in {R}}}, \end{aligned}$$ where $$N\ge 2$$ and f is a sufficiently smooth function satisfying $$f(0)=0$$ , $$f'(0)<0$$ some natural additional conditions. prove that (1) possesses uncountably many positive solutions (disregarding translations) which are radially symmetric in ...

A sentence σ ∈ L ω1,ω is a counterexample to Vaught's Conjecture, or simply a counterexample, if ℵ 0 < I(σ, ℵ 0) < 2 ℵ0 , i.e., σ has uncountably many countable models but fewer than continuum many models. Fix σ a counterexample. A key fact about counterexamples is that there are few types for any count-able fragment. Let F be a fragment. Let

Abstract In this paper, we construct uncountably many examples of multiparameter CCR flows, which are not pullbacks $1$ -parameter with any given index. Moreover, the constructed flows type I in sense that associated product system is smallest subsystem containing its units.

Abstract We prove that many seemingly simple theories have Borel complete reducts. Specifically, if a countable theory has uncountably one-types, then it reduct. Similarly, $Th(M)$ is not small, $M^{eq}$ reduct, and T $\omega $ -stable, the elementary diagram of some model

Abstract We develop a method for showing that various modal logics are valid in their countably generated canonical Kripke frames must also be uncountably ones. This is applied to many systems, including the of finite width, and broader class multimodal ‘finite achronal width’ introduced here.