All Questions
Tagged with ordinal-analysis ordinal-numbers
6 questions
40
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Is there a computable ordinal encoding the proof strength of ZF? Is it knowable?
In comments on Quora (see, for example, here, here, here), Ron Maimon has repeatedly expressed the strong opinion that Hilbert's program was not killed by Gödel's results in the way typically ...
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4
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0
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Ordinal analysis and nonrecursive ordinals
Ordinal analysis is typically described as characterizing recursive ordinals in a theory $T$, but there is a sense in which it can characterize all $T$-ordinals, even those that are nonrecursive.
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- 7,545
8
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Formalizations of The Matchstick Diagram Representation of Ordinals
The matchstick diagram is a really interesting and intuitive method of representing countable ordinals. However, because of how difficult it is to graphically represent ordinals with it, I started ...
- 1,252
16
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answer
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Proof theoretic ordinal
In Ordinal Analysis, Proof-theoretic Ordinal of a theory is thought as measure of a consistency strength and computational power.
Is it always the case? I. e. are there some general results about ...
- 161
13
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3
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Which ordinals can be proof-theoretic ordinals of a reasonable theory?
When talking to a friend recently he asked a question - are there any reasonable first-order theories which have proof theoretic ordinal equal to small or large Veblen ordinal? I have then extended ...
- 28.2k
5
votes
1
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How closely do ordinal collapsing functions relate to Mostowski collapse?
Ordinal collapsing functions (such as Rathjen's $\psi_\pi$-functions, not the Levy collapse function) name large countable ordinals by mapping larger ordinals below some "large" ordinal, ...
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