Timeline for What is Realistic Mathematics?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Dec 2, 2017 at 11:33 | comment | added | Erfan Khaniki | @Neel Krishnaswami: Is there any reference for the relation between large cardinals and termination of programs in a specific programing language? | |
| Dec 26, 2015 at 23:55 | comment | added | Paul Larson | This is very interesting. Which large cardinals are used in this way? Can anyone point me to a reference? | |
| Aug 8, 2010 at 14:28 | comment | added | Per Vognsen | Great answer. You want higher infinities for much the same reason you want countable infinity: every real computer is a finite machine but that is missing the point, and indeed the halting problem has more useful things to say about the limits of computers than the pumping lemma. The termination of any given computable function of practical interest relevance can be proven by induction with small ordinals. The ones that individually require large ordinals are part of the package, byproducts of a more convenient category; they're like non-measurable sets in analysis in that sense. | |
| Aug 8, 2010 at 11:56 | comment | added | Andreas Thom | I agree. If some mathematical notion or concept is useful for some practical purpose like the design of programming languages, then I would would call it realistic. I think, my statement about large cardinals was to broad. Maybe I should have asked instead what properties of large cardinals are the useful ones, when it comes to any sort of practical applications or any relation with the real world. The question is: Is it possible to agree on a mathematics which could be called realistic. More concretely: What properties of large cardinals do you consider useful. | |
| Aug 8, 2010 at 11:44 | history | answered | Neel Krishnaswami | CC BY-SA 2.5 |