Re: Equal Sets and Identical Sets

On 2008-03-14, in sci.logic, MoeBlee wrote:
So in such a context, we don't know whether by "a model for set
theory" we mean one in which '=' must map to the identity relation
on the universe or one in which '=' very well might not map to the
identity relation on the universe. That ambiguity now is puzzling
me. How do I know which of the two options the author intends when
he says something like "consider a model for ZF"?

Can you give any example of a context where this ambiguity would
result in confusion or mathematical difficulties? In any case, taking
identity to be a logical primitive seems pretty much the universal
convention.

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.

Relevant Pages

  • Re: Set theory and identity theory
    ... identity relation on the universe. ... treated as from identity theory and with the ordinary fixed semantics ... so that the model must map '=' to the identity relation on the universe ...
    (sci.logic)
  • Re: Equal Sets and Identical Sets
    ... theory" we mean one in which '=' must map to the identity relation ... identity relation on the universe. ... Can you give any example of a context where this ambiguity would ...
    (sci.logic)
  • News: Best ever map of the early universe revealed
    ... Best ever map of the early universe revealed ... inflation the universe would still be a featureless cloud of gas. ... The polarisation reveals just how ...
    (talk.origins)
  • Largest Map of Universe Yet Bolsters Theories about Dark Energ
    ... Largest Map of Universe Yet Bolsters Theories about Dark Energy ... Using the light of distant, dying galaxies, astronomers have produced ...
    (sci.physics)
  • Re: I feel a twin paradox coming on
    ... In order to allow QM to fit in a universe modelled by general relativity ... over the map of the universe of the detector. ... A potentially fatal flaw for this connection is to ask why this ... It would appear as an extra term in a doppler ...
    (uk.business.agriculture)
Quantcast