Timeline for Lascar strong types in fragments of arithmetic
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jun 21, 2015 at 21:36 | comment | added | tomasz | @EmilJeřábek: Ah. Indeed, that makes it trivial. Thanks for the clarification. | |
| Jun 21, 2015 at 21:03 | comment | added | Domenico Zambella | @tomasz 1.Type definability of the Lascar strong type is only mildly related to tameness/wildness (cfr. the comment of Emil Jeřábek). 2. Full induction means induction for all first-order formulas. Fragments have induction only for formulas in some fixed complexity class. | |
| Jun 21, 2015 at 20:34 | comment | added | Emil Jeřábek | @tomasz: The point is that full induction implies the existence of definable Skolem functions, in which case $M$ can be fixed as the Skolem hull/definable closure of $A$. | |
| Jun 21, 2015 at 19:35 | comment | added | tomasz | It should also be pointed out that the Lascar strong types are type-definable iff components of the Lascar graph have uniformly bounded diameter. What do you mean by full induction? I'm not very familiar with theories of arithmetic, but it seems like it would be odd for them to be G-compact, considering they are rather wild. | |
| Jun 21, 2015 at 19:28 | comment | added | tomasz | The usual definition of the Lascar graph is slightly different (and not equivalent, afaik): an edge connects two points if they are two elements of an infinite indiscernible sequence. The connected components are the same, though. | |
| Jun 21, 2015 at 10:09 | history | asked | Domenico Zambella | CC BY-SA 3.0 |