In model theory, a stable group is a group that is stable in the sense of stability theory. An important class of examples is provided by groups of finite Morley rank (see below).ExamplesA group of fi ...
Let T be a first-order, countable, complete theory with infinite models. Let I(T, \alpha) denote the number of models of T of cardinality \alpha up to isomorphism, the spectrum of the theory T. Morley ...
This article focuses on finitary first order model theory of infinite structures. Finite model theory, which concentrates on finite structures, diverges significantly from the study of infinite struct ...
A cellular automaton consists of a regular system of cells, each containing a symbol from a finite alphabet, together with a uniform rule called a transition function for updating all cells simultaneo ...
Initial work pointed towards the affirmative answer. For example, if a group G is generated by m elements and the order of each element of G is a divisor of 4, then G is finite. Moreover, A. I. Kostri ...
There is a great deal of detailed information in particular cases. It is known that every finite group is realizable over any function field in one variable over the complex numbers C, and more genera ...
One of the interesting properties of periodic groups is that they cannot be formalized in terms of first-order logic. This is because doing so would require an axiom of the form \forall x ((x=e) \lor ...
A free group on a set S is a group where each element can be uniquely described as a finite length product of the form:s_1^{a_1} s_2^{a_2} \ldots s_n^{a_n}where the si are elements of S, adjacent si a ...
Group theory has three main historical sources: number theory, the theory of algebraic equations, and geometry. The number-theoretic strand was begun by Leonhard Euler, and developed by Gauss's work o ...
Subdividing every edge of a graph into two-edge paths can significantly reduce its book thickness. For instance, the book thickness of the complete graph Kn is Θ(n), but subdividing each of its edges ...
If a graph H has an embedding into the projective plane, then it necessarily has a planar cover, given by the preimage of H in the orientable double cover of the projective plane, which is a sphere. N ...
A linear thrackle is a thrackle drawn in such a way that its edges are straight line segments. Every linear thrackle has at most as many edges as vertices, a fact that was observed by Paul Erd?s. Erd ...
Let G be any graph with maximum degree d and diameter k, and consider the tree formed by breadth first search starting from any vertex v. This tree has 1 vertex at level 0 (v itself), and at most d ve ...
The usual formulation of the cycle double cover conjecture asks whether every bridgeless undirected graph has a collection of cycles such that each edge of the graph is contained in exactly two of the ...
The reconstruction conjecture of Stanislaw Ulam is one of the best-known open problems in graph theory. Using the terminology of Frank Harary it can be stated as follows: If G and H are two graphs on ...
