FOM: essentially algebraic; worse than Simpson
Colin Mclarty
cxm7 at po.cwru.edu
Sun Mar 15 11:56:09 EST 1998
Reply to message from friedman at math.ohio-state.edu of Sun, 15 Mar
>Well, let's look at the logical complexity (in this sense) of the axioms
>for topoi given by McLarty'posting of 9:21AM 2/6/98 Challenge axioms, final
>draft.
>
>1. A
>2. AE
>3. A
>4. AEA
>5. A
>6. AEA
>7. A
>8. axiom missing or nonexistent
>9. AEA
>10. AEA
>11. AE
>12. AEAEA
>13. EAEA
>14. AE
>15. AEA
>
These are not the topos axioms. They are axioms for a
particular kind of topos specified in your challenge.
>This is definitely not "essentially algebraic."
No, it is not. You have to remember your challenge,
which specified axioms in standard first order logic. Standard
first order logic does not use partially defined terms, while
I suppose everyone knows that category theory is most simply
described using partially defined terms, and an essentially
algebraic presentation uses partially defined terms.
Challenges are generally not a helpful means of discussing
an issue, because they tend to constrain it to the challenger's
way of looking at it. But they are especially unhelpful when the
challenger forgets what the challenge was and complains that the
response does not also answer some quite different question.
Colin
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