منابع مشابه
Computability and uncountable Linear Orders II: degree spectra
We study the computable structure theory of linear orders of size א1 within the framework of admissible computability theory. In particular, we study degree spectra and the successor relation.
متن کاملThe uncountable spectra of countable theories
Let T be a complete, first-order theory in a finite or countable language having infinite models. Let I(T, κ) be the number of isomorphism types of models of T of cardinality κ. We denote by μ (respectively μ̂) the number of cardinals (respectively infinite cardinals) less than or equal to κ. Theorem I(T, κ), as a function of κ > א0, is the minimum of 2 κ and one of the following functions: 1. 2...
متن کاملUncountable families of vertex-transitive graphs of finite degree
Recently the following question was relayed [1] to the second author: What is the cardinality of the set of vertex transitive graphs of finite degree? Our aim in this short note is to show that there are 20 such graphs. Our proof is constructive and is based on ideas of B. Neumann [3]. In order to construct a large such set it is natural to turn to Cayley graphs of finitely generated groups (se...
متن کاملRelativized Degree Spectra
We present a relativized version of the notion of a degree spectrum of a structure with respect to finitely many abstract structures. We study the connection to the notion of joint spectrum. We prove that some properties of the degree spectrum as a minimal pair theorem and the existence of quasi-minimal degrees are true for the relative spectrum.
متن کاملBounded degree and planar spectra
The finite spectrum of a first-order sentence is the set of positive integers that are the sizes of its models. The class of finite spectra is known to be the same as the complexity class NE. We consider the spectra obtained by limiting models to be either planar (in the graph-theoretic sense) or by bounding the degree of elements. We show that the class of such spectra is still suprisingly ric...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1991
ISSN: 0168-0072
DOI: 10.1016/0168-0072(91)90049-r