Timeline for The isomorphism inference rule
Current License: CC BY-SA 2.5
2 events
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| Jun 19, 2010 at 11:59 | comment | added | Carl Mummert | It requires that there is an equivalence relation that preserves the structures which happen to be definable by the theory in question. This is why we can define an equality relation satisfying Leibniz's rule in ZFC: because anything we can define using only ∈ will respect extensional equality. But it's perfectly possible for Leibniz's rule to hold in a structure for which = is not interpreted as true equality, in which case it does not capture everything. However, by convention, we always mod out by = so that the = symbol does represent actual equality. | |
| Jun 19, 2010 at 11:30 | history | answered | Niel de Beaudrap | CC BY-SA 2.5 |