When must it be sets rather than proper classes, or vice-versa, outside of foundational mathematics?
Every once in a blue moon it actually matters that some mathematical entity which might a priori only be a class is in fact a set. For clarification, here are some examples of what I do not ...
Much of the research taking place in set theory, is related to the classification of sentences according to their consistency strength relative to ZF. In order to be more specific, we say that for all ...
You might think that the title is an overstatement of a well-known fact but it is the best title I can come up with for the wonders the intersection operator does in some fields of math. ...
Of all the constructions of the reals, the construction of the surreals seems the most elegant to me. It seems to immediately capture the total ordering and precision of Dedekind cuts at a ...
Every student of set theory knows that the early axiomatization of the theory had to deal with spectacular paradoxes such as Russel's, Burali-Forti's etc. This is why the (self-contradictory) ...
Strongly inaccessible cardinals are usually introduced either as (a) cardinalities of models of ZFC or (b) cardinals which are not the power set of a smaller cardinal nor the supremum of a set with ...
Motivation The usual starting point of both Topology and Measure Theory is the definition of a family of subsets of a set $S$. Indeed, one defines a topology on $S$ to be a family of subsets ...
I've been reading some "introduction to categories" type materials and have been impressed with the all-encompassing nature, but the skeptic in me wonders: is there any mathematical object that ...