Let L be a finite first-order language and 〈Mn | n < ω〉 be a sequence of finite L-models containing models of arbitrarily large finite cardinality. If the intersection of less than continuum-many dense open subsets of Cantor Space 2 is non-empty, then there is a non-principal ultrafilter U over ω such that the corresponding ultraproduct Q U Mn is infinite and has an automorphism that is not ind...

It is shown that the positive first-order theory of an HNN-extension G = 〈H, t; tat = φ(a)(a ∈ A)〉 can be reduced to the existential firstorder theory of G provided that A and B are proper subgroups of the base group H with A∩B finite. For an amalgamated free product G = H ∗A J , we show that the positive first-order theory of G can be reduced to the existential first-order theory of G in case ...

Recent work by Procaccia, Rosenschein and Zohar [14] established some results regarding the complexity of manipulation and control in elections with multiple winners, such as elections of an assembly or committee; that work provided an initial understanding of the topic. In this paper, we paint a more complete picture of the topic, investigating four prominent multi-winner voting rules. First, ...

Some structural properties as well as a general threedimensional boundary value problem for normally hyperbolic systems of partial differential equations of first order are studied. A condition is given which enables one to reduce the system under consideration to a first-order system with the spliced principal part. It is shown that the initial problem is correct in a certain class of function...

We study categoricity in power for reduced models of first order logic without equality.

In this article, we formalize some basic facts of Z-module. In the first section, we discuss the rank of submodule of Z-module and its properties. Especially, we formally prove that the rank of any Z-module is equal to or more than that of its submodules, and vice versa, there exists a submodule with any given rank that satisfies the above condition. In the next section, we mention basic facts ...

The aim of this paper is to give a new proof for the decidability and nite model property of rst-order logic with two variables (without function symbols), using a combinatorial theorem due to Herwig. The results are proved in the framework of polyadic equality set algebras of dimension two (Pse 2). The new proof also shows the known results that the universal theory of Pse 2 is decidable and t...

We introduce a proper display calculus for (non-distributive) Lattice Logic which is sound, complete, conservative, and enjoys cut-elimination and subformula property. Properness (i.e. closure under uniform substitution of all parametric parts in rules) is the main interest and added value of the present proposal, and allows for the smoothest Belnap-style proof of cut-elimination. Our proposal ...

The result of forgetting some predicates in a first-order sentence may not exist in the sense that it might not be captured by any first-order sentences. This, indeed, severely restricts the usage of forgetting in applications. To address this issue, we propose a notion called k-forgetting, also called bounded forgetting in general, for any fixed number k. We present several equivalent characte...