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Results tagged with set-theory
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user 14490
forcing, large cardinals, descriptive set theory, infinite combinatorics, cardinal characteristics, forcing axioms, ultrapowers, measures, reflection, pcf theory, models of set theory, axioms of set theory, independence, axiom of choice, continuum hypothesis, determinacy, Borel equivalence relations, Boolean-valued models, embeddings, orders, relations, transfinite recursion, set theory as a foundation of mathematics, the philosophy of set theory.
3
votes
Accepted
Problem with definability in the constructible hierarchy
I may have found where is the trick hidden: I mean two different things by "being $\Sigma_2$-definable". When I write "the smallest ordinal which is not $\Sigma_2$-definable" I mean being definable by …
- 764
2
votes
1
answer
1k
views
Consistency and inaccessible cardinals [closed]
I just want to make sure I understand certain things well. I believe my questions are quite simple. Are the following statements true?
1/ One cannot prove Con(ZFC) in ZFC. However ZFC might not be co …
- 764
6
votes
1
answer
473
views
Problem with definability in the constructible hierarchy
This is a rather technical question. I cannot find my mistake in a proof of the (obviously wrong) following sentence: Every countable ordinal is $\Sigma_2$-definable in $J_{\omega_1 + 1}$ by a formula …
- 764
5
votes
1
answer
617
views
On a characterization of the recursively inaccessible ordinals
For a given set of numbers $A$, let $O^A$ be the hyperjump of $A$. It is possible to iterate inductively the hyperjump of a set, through the computable ordinals, in a way that the $\alpha$-th hyperjum …
- 764
2
votes
Accepted
On a characterization of the recursively inaccessible ordinals
Well assuming that $\lambda^A$ is always the first recursively admissible which is bigger than $\omega_1^A$, which I think should be true, I think my question is after all not so interesting:
Either …
- 764
2
votes
Accepted
Higher computability : Constructive ordinal and $\Delta^1_1$ predicates
I finaly got an answer from another forum.
The answer is simple, I was assuming that if $A \subseteq \omega$ is $\Delta^1_1(Y)$ it means that there is a $\Pi^1_1$ predicate $F \subseteq \omega \times …
- 764
5
votes
1
answer
412
views
Higher computability : Constructive ordinal and $\Delta^1_1$ predicates
Everything I know on this subject comes from Sacks book : "Higher recursion theory"
Let $\mathcal{O^Y}$ be the set of codes for ordinals constructive in $Y$.
We should have the result that $A \subse …
- 764