All Questions
7 questions
2
votes
1
answer
204
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Ordinal notations in α-recursion theory
Is there a theory about using α-recursion to compute ordinals?
For example, consider α-recursive well orders on α, what is the supreme of their order type? Is it the next admissible ordinal after α? ...
- 2,031
3
votes
0
answers
368
views
An alternative definition of computable ordinals
An ordinal $\alpha$ is said to be computable if there is a computable relation on a subset of integers that is well-ordered and its order type equals $\alpha$.
But let's consider well-founded trees on ...
- 2,031
4
votes
1
answer
268
views
Existence of a particular function that maps an arbitrary set of ordinals to a single ordinal
Does there exist a function $f$ that satisfies all of the following three properties?
The function converts an arbitrarily large (empty, finite, countably/uncountably infinite) set of ordinals to a ...
- 17.7k
6
votes
0
answers
303
views
Weaker versions of Gandy ordinals
Gostanian's paper "The next admissible ordinal" (see https://www.sciencedirect.com/science/article/pii/0003484379900251 ), is concerned with the supremum of the $\alpha$-recursive ordinals for various ...
- 365
9
votes
1
answer
711
views
Computable models of the ordinal numbers
It's known, for example in the answer to this question: Is there a computable model of ZFC? that ZFC has no computable model. My questions is: is there a model of ZFC for which the order relation on ...
- 21.2k
4
votes
2
answers
591
views
Connection between countable ordinals and Turing degrees
$\omega^{CK}_1$ is the supremum of all the recursive ordinals, where an ordinal $\alpha$ is recursive if there is a computable ordering of a subset of the naturals with order type $\alpha$.
For a ...
- 4,201
4
votes
0
answers
199
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On the proof of a normal form theorem for ordinal (primitive) recursion
Consider the following statement (which follows easily from various results found in the literature):
(†) There exists a primitive recursive (“p.r.”) relation $T$ on the ordinals such that, if $(...
- 32.5k