Timeline for Reference wanted for the theory of pseudofinite models
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 1, 2011 at 18:14 | vote | accept | Benjamin Steinberg | ||
| Aug 1, 2011 at 18:14 | comment | added | Benjamin Steinberg | Thanks guys. This answers all my questions once I learn how EF games work. | |
| Aug 1, 2011 at 13:57 | comment | added | Andreas Blass | @Benjamin, concerning your first comment: My experience with pseudofiniteness is quite limited, but so far, yes, I've found E-F games to be a good way to think about elementary equivalence (in that context and also in other situations). Concerning your second comment: I'd say the theory of finite orders means all the first-order sentences true in all finite orders; it is then a theorem that this theory is axiomatized by these three axioms plus the defining axioms for linear orders. | |
| Aug 1, 2011 at 13:17 | comment | added | Emil Jeřábek | @Benjamin: denote the theory (i.e., the three axioms + the axioms of linear orders) as $T$, and let $A$ be a sentence valid in all finite orders. Then $A$ is valid in all finite models of $T$. By compactness, it is also valid in some infinite model of $T$. By Andreas’ argument, it is then valid in all infinite models of $T$, hence in all models of $T$. | |
| Aug 1, 2011 at 11:33 | comment | added | Benjamin Steinberg | How does one prove that all formulas satisfied by finite orders are consequences of the 3 axioms you give? Or alternatively, how do you see each order of the above form is an ultraproduct of finite orders? I'm very far from model theory, so although I'm sure this is elementary it would be nice to see it (or a reference). | |
| Aug 1, 2011 at 10:39 | comment | added | Benjamin Steinberg | I should add I was pretty sure that the theory of finite orders meant exactly first and last element and that any other element had a predecessor and successor. Is it completely obvious that all such orders have the form stated. I guess so. The first N is all successors of the first guy, the last N* is all predecessors of the last guy and for each other guy, its predecessors and successors from a copy of Z. | |
| Aug 1, 2011 at 10:36 | comment | added | Benjamin Steinberg | Thanks. Are Ehrenfeucht-Fraisse games in general a good way to check if two pseudofinite structures are elementarily equivalent? | |
| Aug 1, 2011 at 3:42 | history | answered | Andreas Blass | CC BY-SA 3.0 |