# Tag Info

1 vote

### Notion of independence of Turing degrees

Rather belatedly, I should probably mention that Uri Andrews, Peter Gerdes, Steffen Lempp, Joe Miller, and I have written a paper on this: Computability and the symmetric difference operator (DOI); ...
• 21.8k
1 vote

• 30.1k
Accepted

### Are equinumerous size preserving models of a theory isomorphic?

There is no version of this question I can think of which has an affirmative answer. Let $\alpha,\beta$ be distinct countable ordinals such that $L_\alpha\equiv L_\beta\equiv L_{\omega_1^L}$ (which ...
• 21.8k
Accepted

• 14.8k
Accepted

### How do chains of elementary extensions compare to shrewdness?

As Cantor's Attic explains, if $\kappa$ is 0-uplifting, that is, there is a cardinal $\lambda \gt \kappa$ such that $V_\kappa \prec V_\lambda$ and $\lambda$ is inaccesible, $\lambda$ has a club subset ...

### Tarski's original proof of quantifier elimination in algebraically closed fields

Passmore's PhD thesis has an introductory section developing an elementary quantifier elimination algorithm for algebraically closed fields of characteristic zero "from scratch" with much ...
Accepted

### Tarski's original proof of quantifier elimination in algebraically closed fields

I doubt you’ll find a shorter proof than Swan’s which is equally elementary. In particular: For algebraically closed fields, you can stop in the middle of page 10 of the document, which should make ...
• 16.6k
Accepted

### Properties of Jech's hierarchy of stationary sets (Exercise 8.13, 8.14 of Jech)

After some googling I found the notes by J. D. Monk, which have answered the questions in the span of Theorem 2.68 to 2.91.
• 634
Accepted

### What's the consistency status/strength of this limitation principle?

This principle is inconsistent: consider the formula $\theta(x)$ = "$x^+$ is the smallest infinite cardinal at which $\mathsf{CH}$ fails." The formula $\theta$ cannot hold on more than one ...
• 21.8k
Accepted

### Linear logic and linearly distributive categories

Yes, Cockett and Seely's comment about proof theory is a reference to the theory/category adjunction. Each kind of theory corresponds to a kind of category, for instance: Theory Category simply ...
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### Has there been any mathematical study of causality?

I am converting my comments into an answer. Setting aside the alleged parallel between causation and inference for a moment, there has indeed been some mathematical investigation of cause and effect. ...
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