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Results tagged with ordinal-analysis
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user 479330
2
votes
0
answers
185
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How closely do ordinal collapsing functions relate to Skolem hulls?
Ordinal collapsing functions appear in proof theory, and they are used to name large countable ordinals by using uncountable ordinals. Previously I posted a question about why $\psi(\alpha)$ is someti …
- 2,031
5
votes
1
answer
297
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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, often chosen …
- 2,031
1
vote
How closely do ordinal collapsing functions relate to Mostowski collapse?
This description seems to be a closer connection to Mostowski collapse than "it is the order type of $C_\Omega(\alpha,\rho)$ when some elements are removed":
A similar comparison appears in Toshiyasu …
- 2,031
5
votes
Iterated Gentzen: or, a Sith objection to the proof of consistency of PA
Mathobi is making a different argument in the comments on this post than in the question itself: in the post Mathobi is considering how far we need to justify transfinite induction to prove $G(i)$ con …
- 2,031
3
votes
What is the proof-theoretic ordinal of KPh?
Let $\mathsf{KPh}$ denote the theory $\mathsf{KP}+``\textrm{The recursively inaccessibles are unbounded}\! "$. I haven't found an explicit analysis of $\mathsf{KPh}$ in Rathjen's preprints, but there …
- 2,031
6
votes
0
answers
175
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Iterated $\Pi^1_1$-reflection and non-Gandiness underrepresented in ordinal analyses?
This is a copy of Math StackExchange question #4395977, which I felt was more appropriate for MathOverflow.
Note on terminology: "admissible", "$(^+)$-stable", and "$\Pi^1_1$-reflecting" can all be fo …
- 2,031
2
votes
Which ordinals can be proof-theoretic ordinals of a reasonable theory?
$\newcommand{\bomega}{\boldsymbol\omega}$Given the definition of bounding ordinal in the post and the potential sensitivity to coding mentioned in edit 2, these seem to be two main ways to formalize b …
- 2,031