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2:18 PM
@LeakyNun I don't trust all my memories. However, this is where logic can be put to good use: (1) If you develop a heavily interconnected web of logical connections between a bunch of scenes and entities that you witnessed, it becomes much harder for you to remember something wrongly because you can self-correct easily using logic. (2) If you always endeavour to act or respond strictly according to your principles, and your principles have logical foundations, then it is easy to re-derive a lot.
These two factors are in fact why I can trust many of my more important memories, namely the ones about issues that I care a lot about, because I've thought about them logically a lot. Mundane stuff I forget all the time!
 
 
2 hours later…
4:24 PM
Hi everyone, I'm looking for a simple example of two models of the same cardinality of a theory which are partially isomorphic but not isomorphic, is there a simple example? By Scott's isomorphism theorem that can't happen if those models are countable
And I know examples of structures of different cardinalities which are partially isomorphic but not isomorphic, for example $(\Bbb R,<)\simeq_p(\Bbb Q,<)$
 

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