All Questions
3 questions
2
votes
0
answers
133
views
Higher-order oracle computation of reals and axiom of constructibility
Certain real numbers can be approximated arbitrarily well by computable functions. If we introduce halting oracles, then more real numbers can be "computed", like Chaitin's constant or the ...
- 173
9
votes
3
answers
2k
views
What set theoretical questions could never be answered by Turing machines of arbitrary cardinality?
Let us assume that there are Turing machines of arbitrary cardinality, by that I mean they can have input tapes of any arbitrarily high cardinality and compute for a number of steps also of ...
- 437
2
votes
1
answer
609
views
Would a non-constructible set become constructible if we had oracles of arbitrarily high cardinality for the halting problems of ordinal computers?
I still have trouble to grasp the concept of a non-constructible set, my intuition is that we could "avoid" the non-constructibility of many of them if we assume we have "ordinal computers" extended ...
CommunityBot
- 1