Timeline for The question about elementary equivalence of free products
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| May 11, 2020 at 8:11 | history | edited | YCor |
edited tags; edited tags
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| May 11, 2020 at 6:08 | comment | added | Emil Jeřábek | @YCor Mostowski, On direct products of theories, Journal of Symbolic Logic 17 (1952), 1–31. The Feferman–Vaught theorem is a considerable generalization: Feferman, Vaught, The first order properties of products of algebraic systems, Fundamenta Mathematicae 47 (1959), 57–103. | |
| May 10, 2020 at 21:49 | comment | added | YCor | @EmilJeřábek Do you have a reference? I'm aware of a quite indirect proof, making use of ultraproducts and absoluteness. | |
| May 10, 2020 at 21:47 | comment | added | YCor | I guess it's meant universal algebraic systems (with only laws, no relations) otherwise I don't see how to define the free products. | |
| Apr 2, 2019 at 17:12 | answer | added | HJRW | timeline score: 5 | |
| Apr 2, 2019 at 13:24 | comment | added | James E Hanson | If the structures are $\omega$-saturated then you should be able to argue with Ehrenfeucht-Fraïssé games that the resulting free products are elementarily equivalent. This is only non-trivial if the structures are uncountable, though. | |
| Apr 2, 2019 at 11:31 | comment | added | Emil Jeřábek | I assume you already know this, but the answer is positive for direct (Cartesian) products of arbitrary first-order structures. | |
| S Apr 2, 2019 at 9:29 | history | suggested | Daniele Tampieri | CC BY-SA 4.0 |
Math Jaxed and formatted
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| Apr 2, 2019 at 9:08 | review | Suggested edits | |||
| S Apr 2, 2019 at 9:29 | |||||
| Apr 2, 2019 at 7:55 | review | First posts | |||
| Apr 2, 2019 at 9:08 | |||||
| Apr 2, 2019 at 7:52 | history | asked | Evgeny | CC BY-SA 4.0 |