Timeline for Generalizations of Birkhoff's HSP Theorem
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Dec 2, 2013 at 23:07 | comment | added | bof | In the same vein as Birkhoff and Lyndon, Weinstein proved that a first-order sentence is preserved by direct products AND unions of chains if and only if it's logically equivalent to a universal-existential Horn sentence. This was (if I remember right) the main result of his dissertation; it's probably mentioned in Chang and Keisler's book. | |
| Dec 2, 2013 at 21:52 | comment | added | bof | Good question. If anybody knows I guess it would be Keisler. Maybe you should ask the great man himself: math.wisc.edu/~keisler | |
| Dec 2, 2013 at 21:49 | comment | added | bof | mathoverflow.net/help/someone-answers | |
| Dec 2, 2013 at 18:31 | comment | added | Tristan Bice | However, I would still be curious to know if there is some nice description of sentences that are both a product AND a factor sentence. After all, Birkhoff's HSP theorem and Lyndon's HD(=HP) theorem show that adding assumptions to "product sentence" can lead to simpler characterizations. | |
| Dec 2, 2013 at 18:26 | comment | added | Tristan Bice | Great, thanks for the references. I couldn't find the results themselves in Chang and Keisler's book, although they do say there that Weinstein's thesis contains some complicated characterization of product sentences, as you mentioned, and exercise 5.2.23** is about characterizing factor sentences, which is explained in more detail in Keisler's article "Some Applications of Infinitely Long Formulas". | |
| Dec 1, 2013 at 23:20 | history | edited | bof | CC BY-SA 3.0 |
added 3 characters in body
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| Dec 1, 2013 at 23:13 | history | answered | bof | CC BY-SA 3.0 |