Timeline for Can the equational theory of commutative rings be "unpacked" from the equational theory of exponentiation?
Current License: CC BY-SA 4.0
6 events
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| Oct 16, 2022 at 10:48 | comment | added | Noah Schweber | @tomasz That's a fair point, but $\mathcal{V}$ comes into play when we interpret the unpack (as $T_\mathcal{V}(\mathfrak{E})$). | |
| Oct 16, 2022 at 10:46 | comment | added | tomasz | It's a bit odd that your definition of a $\mathcal V$-unpacking does no really depend on $\mathcal V$ (only on $\Sigma$). Or am I missing something? | |
| Oct 15, 2022 at 18:40 | comment | added | user44143 | How about “Given languages $L$ and $L’$, define an unpacking of the $L$-model $M$ into the $L’$-theory $T$ as an $L+L’$-theory $U$ whose restriction to $L$ is the theory of $M$, whose restriction to $L’$ is the theory $T$, and which is axiomatized by equations whose left sides are contained in $L$. Then, considering the languages $\wedge$ and $\{\oplus, \otimes\}$, is there an unpacking of $\mathbb{N}$ (under exponentiation) into the theory of commutative rings?” | |
| Oct 15, 2022 at 17:58 | comment | added | Noah Schweber | @MattF. Well, the thing I'm primarily interested in is the general notion of unpacking. This is really only a test question - I'm hopeful that it will provide an interesting example in one direction or the other, but the general notion is what I really care about. | |
| Oct 15, 2022 at 15:38 | history | edited | Noah Schweber | CC BY-SA 4.0 |
added 281 characters in body
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| Oct 15, 2022 at 4:13 | history | asked | Noah Schweber | CC BY-SA 4.0 |