A countable Fréchet–Urysohn space of uncountable character
نویسندگان
چکیده
منابع مشابه
The Countable Character of Uncountable Graphs
We show that a graph can always be decomposed into edge-disjoint subgraphs of countable cardinality in which the edge-connectivities and edge-separations of the original graph are preserved up to countable cardinals. We also show that the vertex set of any graph can be endowed with a well-ordering which has a certain compactness property with respect to edge-separation.
متن کاملCohesive Sets: Countable and Uncountable
We show that many uncountable admissible ordinals (including some cardinals) as well as all countable admissible ordinals have cohesive subsets. Exactly which cardinals have cohesive subsets, however, is shown to depend on set-theoretic assumptions such as V=L or a large cardinal axiom. The study of recursion theory on the ordinals was initiated by Takeuti and then generalized by several others...
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 کاملThe Basic Trichotomy: Finite, Countable, Uncountable
Fact 1. The set Z is infinite. Proof: It is certainly nonempty, so we would like to show that for no n ∈ Z is there a bijection ι : [n] → Z. This seems obvious. Unfortunately, sometimes in mathematics we must struggle to show that the obvious is true (and sometimes what seems obvious is not true!). Here we face the additional problem of not having formally axiomatized things, so it’s not comple...
متن کاملReverse mathematics, countable and uncountable: a computational approach
Reverse mathematics analyzes the complexity of mathematical statements in terms of the strength of axiomatic systems needed to prove them. Its setting is countable mathematics and subsystems of second order arithmetic. We present a similar analysis based on (recursion theoretic) computational complexity instead. In the countable case, this view is implicit in many of results in the area. By mak...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2008
ISSN: 0166-8641
DOI: 10.1016/j.topol.2008.02.001