Timeline for "Tietze-like transformations" for defining interesting bijections between algebraic structures
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 7, 2021 at 15:43 | vote | accept | Sophie Swett | ||
| Aug 29, 2020 at 16:09 | answer | added | varkor | timeline score: 3 | |
| Aug 25, 2020 at 22:16 | comment | added | Sophie Swett | @KeithKearnes I've edited the question to remove all references to that ill-defined notion of equivalence. Hopefully the question is clearer now. | |
| Aug 25, 2020 at 22:15 | history | edited | Sophie Swett | CC BY-SA 4.0 |
Rewrite in terms of bijections instead of "equivalence"; try to make other clarifications
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| Aug 25, 2020 at 20:32 | comment | added | Sophie Swett | @KeithKearnes I can't give a real definition of what I mean by "equivalent" or "reasonably chosen"; they aren't well-defined concepts. However, I've thought of a way to make the question clearer by removing this vague terminology. I plan to edit the question soon. | |
| Aug 25, 2020 at 20:10 | comment | added | Keith Kearnes | What does 'reasonably chosen' mean? | |
| Aug 25, 2020 at 19:01 | comment | added | Sophie Swett | @KeithKearnes Suppose we have two algebraic structures $A$ and $B$. (By "algebraic structure" I mean an individual algebra, not a variety of algebras or an algebraic theory.) Then I call $A$ and $B$ equivalent if there is some "reasonably chosen" algebraic structure $C$ such that $A$ is simply $C$ with some of the operations removed, and $B$ is also simply $C$ with some of the operations removed. In the natural numbers example here, $A = (\mathbb{N}, 0, S)$, $B = (\mathbb{N}, 0, 1, P)$, and $C = (\mathbb{N}, 0, 1, P, S)$ (where $P$ is the addition operation and $S$ is the successor operation). | |
| Aug 25, 2020 at 18:22 | comment | added | Keith Kearnes | What does 'equivalent' mean? | |
| Aug 22, 2020 at 10:58 | history | edited | YCor |
edited tags
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| Aug 22, 2020 at 10:57 | comment | added | YCor | You're defining "the" natural numbers as a structure that is unique up to unique isomorphism, but not unique. | |
| Aug 22, 2020 at 3:08 | comment | added | Sophie Swett | I apologize for the great length of this question, and I would greatly appreciate any suggestions for how to trim it down or to make it easier to understand. | |
| Aug 22, 2020 at 3:07 | history | asked | Sophie Swett | CC BY-SA 4.0 |