7
votes
Accepted
Does every ordinal appearing in a model of ZF appear in a model of ZFC?
As Noah mentioned in the comments, the answer to the first question is "yes".
The answer to the second question is consistently "no", assuming a little consistency: if there is a ...
- 6,549
3
votes
When can interpretations be "optimized"?
The answer to Question 2 is negative and the answer to Question 1 is positive.
In fact the usual interpretation $\Phi$ of $\mathsf{PA}$ in $\mathsf{ZFC}$ is not even weakly optimal. Indeed, consider ...
- 5,303
2
votes
Equational theories determined by "identities without variables"
This question was edited on March 12, 2023 and I was asked to comment on the edited form. Let me copy the essential part of the new question:
I believe $\ldots$ that a variety $\mathscr V$ is of the ...
- 10.4k
1
vote
Accepted
Need proof on a model being elementarily equivalent but non-isomorphic
To show that the models are not isomorphic assume an isomorphism $f:\frak{A}\to\frak{B}$, take $(a_n)_{n\in\omega}$ be an increasing sequence such $a_i,a_j$ are from a different copy of $\Bbb Z$ for ...
- 1,097
1
vote
Is there a metamathematical $V$?
This may be more in line with Vincent R.B. Blazy's answer, but one thing I would like to add is the principle of inexhaustibility. This principle appears in Maddy's "Believing the Axioms. I",...
- 482
1
vote
dp-minimality and stability
This comes a bit late. I just wanted to mention that an interesting family of examples are superflat graphs, proved to be stable by Podewski and Ziegler. See "Computations of Vapnik-Chervonenkis ...
- 131
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