The Cofinality of The Random Graph
نویسنده
چکیده
We show that under Martin’s Axiom, the cofinality cf(Aut(Γ)) of the automorphism group of the random graph Γ is 2ω.
منابع مشابه
The cofinality of the saturated uncountable random graph
Assuming CH, let Γω1 be the saturated random graph of cardinality ω1. In this paper we prove that it is consistent that cf(Aut(Γω1)) and 2ω1 can be any two prescribed regular cardinals subject only to the requirement ω1 < cf(Aut(Γω1)) ≤ 2ω1 .
متن کاملLPKP: location-based probabilistic key pre-distribution scheme for large-scale wireless sensor networks using graph coloring
Communication security of wireless sensor networks is achieved using cryptographic keys assigned to the nodes. Due to resource constraints in such networks, random key pre-distribution schemes are of high interest. Although in most of these schemes no location information is considered, there are scenarios that location information can be obtained by nodes after their deployment. In this paper,...
متن کاملThe uncountable cofinality of the automorphism group of the countable universal distributive lattice
We show that the automorphism group of the countable universal distributive lattice has strong uncountable cofinality, and we adapt the method to deduce the strong uncountable cofinality of the automorphism group of the countable universal generalized boolean algebra.
متن کاملAperiodicity and cofinality for finitely aligned higher-rank graphs
We introduce new formulations of aperiodicity and cofinality for finitely aligned higher-rank graphs $\Lambda$, and prove that $C^*(\Lambda)$ is simple if and only if $\Lambda$ is aperiodic and cofinal. The main advantage of our versions of aperiodicity and cofinality over existing ones is that ours are stated in terms of finite paths. To prove our main result, we first characterise each of ape...
متن کاملOn the Cofinality of Infinite Partially Ordered Sets: Factoring a Poset into Lean Essential Subsets
We study which infinite posets have simple cofinal subsets such as chains, or decompose canonically into such subsets. The posets of countable cofinality admitting such a decomposition are characterized by a forbidden substructure; the corresponding problem for uncountable cofinality remains open.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Symb. Log.
دوره 66 شماره
صفحات -
تاریخ انتشار 2001