Timeline for How necessary is Godel's Condensation Lemma
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jun 27, 2014 at 12:18 | comment | added | Joel David Hamkins | @AndreasBlass That's familiar, then. I suppose that one can replace the Lowenheim-Skolem argument just by closing under the operations, which one can do without increasing the cardinality, and then arguing that the Mostowski collapse is also closed under the operations and hence is some $L_\beta$. | |
| Jun 27, 2014 at 2:37 | comment | added | Andreas Blass | If I remember correctly, Gödel avoided formalizing first-order logic by using what are now called the Gödel operations, a collection of functions that suffice to construct, from a given set, all the sets first-order-definable over it. If you look at the Gödel functions you'll see that some of them correspond to the first-order quantifiers and connectives, and others take care of bookkeeping, like permuting the arguments of a relation. | |
| Jun 27, 2014 at 2:36 | comment | added | Nik Weaver | ... no luck, it is nowhere to be found. | |
| Jun 27, 2014 at 1:15 | comment | added | Nik Weaver | Yeah, I actually thought I had a copy of the book but I couldn't find it just now. I'll go look again. | |
| Jun 27, 2014 at 1:08 | comment | added | Joel David Hamkins | Wow! It would be great if someone could summarize the argument he used. | |
| Jun 27, 2014 at 0:50 | history | answered | Nik Weaver | CC BY-SA 3.0 |