13
votes

Accepted

### A doubt about the Gödel condensation lemma

Your mistake is that taking the Mostowski collapse does not preserve elementarity.
We do have a countable transitive $A$ and a countable $M$ with $$A\cong M\preccurlyeq V_{\omega_1},$$ where $M$ comes ...

8
votes

### On the utility of Silver machines

The existence of morasses using Silver machine in L is proved in the PhD thesis of Thomas Lloyd Richardson, ``Silver Machine Approach to the Constructible Universe''.
See also Silver machines and ...

5
votes

Accepted

### What is a 'power admissible model'?

Stefan, in the paper "The Strength of Mac Lane Set Theory," Mathias says that the notion is due to Harvey Friedman, and essentially coincides with what you describe, except that in KP$^P$, foundation ...

3
votes

Accepted

### Ordering patterns of projecta by least witness

$<_\rho$ is a wellorder essentially by definition. The ordertype is $\omega^{\omega}$ (ordinal exponentiation of course).
In fact $s<_\rho t$ iff either $\mathrm{lh}(s)<\mathrm{lh}(t)$,
or $\...

2
votes

Accepted

### Mitchell, Steel. FSIT. Lemma 2.8: Is $k$-solidity actually needed?

In my question I already verified that (assuming 1. and 2.) item 3. is provable without assuming that $\pi(r)$ is $k$-solid over $(\mathcal{M},q)$. To see that we can actually drop $k$-solidity in ...

1
vote

### On the utility of Silver machines

To begin to answer your 'abstract question', "What are Silver Machines good for', one need only look at the title of Prof. Silver's unpublished manuscript
"How to eliminate the fine ...

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