[FOM] ZC vs. ZFC: a pedagogical perspective

praatika@mappi.helsinki.fi praatika at mappi.helsinki.fi
Sat Jan 30 14:23:15 EST 2010

Lainaus "Jeremy Bem" <jeremy1 at gmail.com>:

> More personally, a peculiarity of my education is that I was
> introduced to ZFC without having independently encountered any math
> that requires replacement.  As such, ZFC was under-motivated.
> (I studied logic at Berkeley, where I was required to pass exams on
> analysis and algebra -- but I don't believe that any of that material
> required replacement.)

But this does not mark a difference between ZFC and ZC ! Much less  
than the latter is needed for developing the ordinary analysis and  
algebra. Even the axiom of infinity can be dropped. Recall that it all  
can be done in ACA_0, which is a conservative extension of PA. There  
is a similar conservative extension of finitary set theory (add  
predicative comprehension) that will also do.

Best, Panu

Panu Raatikainen

Ph.D., Academy Research Fellow,
Docent in Theoretical Philosophy

Department of Philosophy
University of Helsinki

E-mail: panu.raatikainen at helsinki.fi


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