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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