منابع مشابه
Countable Ordinals
This development defines a well-ordered type of countable ordinals. It includes notions of continuous and normal functions, recursively defined functions over ordinals, least fixed-points, and derivatives. Much of ordinal arithmetic is formalized, including exponentials and logarithms. The development concludes with formalizations of Cantor Normal Form and Veblen hierarchies over normal functions.
متن کاملImages of the Countable Ordinals
We study spaces that are continuous images of the usual space [0, ω1) of countable ordinals. We begin by showing that if Y is such a space and is T3 then Y has a monotonically normal compactification, and is monotonically normal, locally compact and scattered. Examples show that regularity is needed in these results. We investigate when a regular continuous image of the countable ordinals must ...
متن کاملMetarecursively Enumerable Sets and Admissible Ordinals
Here we describe some results which will be proved in detail in [13] and [l4]. The notion of metarecursive set was introduced in [8]. Kreisel [7] reported on some of the model-theoretic deliberations which preceded the definitions of [8]. Metarecursion theory is a generalization of ordinary recursion theory from the natural numbers to the recursive ordinals. Theorems about finite sets of natura...
متن کاملPartitioning Pairs of Countable Sets of Ordinals
Lemma 1. There are ω1 disjoint stationary subsets of ω1. Proof. Let Cub(ω1) = {X ⊆ ω1 : ∃C ⊆ X(C is club on ω1)}. Then Cub(ω1) is countably complete filter. Its dual ideal Cub (ω1) = {X ⊆ ω1 : ∃X ′ ∈ Cub(ω1)(X = ω1\X ′)} is countably complete and contains all singletons and so all countable subsets of ω1. Recall also that X ⊆ ω1 is stationary if and only if X / ∈ Cub(ω1). For every ρ < ω1 let f...
متن کاملWalks on Countable Ordinals and Selective Ultrafilters
In our previous work we have introduced filters on the set of countable ordinals as invariants to standard characteristics of walks in this domain. In this note we examine their projections to the set of natural numbers.
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 1985
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000021450