François G. Dorais
Reputation
3,190
Top tag
Next privilege 5,000 Rep.
Approve tag wiki edits
 May7 comment A natural example in category theory This is not an explicit requirement but it is implied: if $X$ is itself inhabited then it is clearly isomorphic to a subobject of an inhabited object. May7 asked A natural example in category theory May7 awarded Caucus Apr26 comment What is Baire's zero-dimensional metric space? Additional context would help, but it's usually this one - en.wikipedia.org/wiki/Baire_space_(set_theory) Apr26 awarded Informed Apr5 comment Uniform distribution with probability density function. Find the value of $k$. How many types of mathematicians are there? Mar27 awarded Good Answer Jan7 comment What are the differences between rings, groups, and fields? That used to be the case but most authors today define a ring to have $1$. The unusual looking term rng is sometimes used for the concept without $1$. Dec27 comment Is empty set a proper subset of itself? $B \setminus A \neq \varnothing$ does not imply that $A$ is a subset of $B$. (But, if it is, then it is indeed a proper subset.) Dec5 answered Questions about generalizations of the Principle of Dependent Choices Dec4 answered Proofs whose length depends on the input Sep18 answered Does every nonempty definable finite set have a definable member? Aug19 answered Borel linear order cannot have uncountable increasing chain Aug19 comment Borel linear order cannot have uncountable increasing chain I had missed the link! The author cites Harrington and Shelah, who did prove the result I recalled earlier. I guess it would be best to check that reference. @William: No. There are no uncountable wellordered Borel chains at all so that weaker variant is vacuously true. Aug19 comment Borel linear order cannot have uncountable increasing chain This is true if chain is replaced by wellordered chain. In other words, a Borel linear order cannot contain a copy of $\omega_1$ or its reverse. I would guess that's what is meant, otherwise "increasing or decreasing" is not very meaningful. Where is this from? Aug16 comment What is actually “relatively consistent”? "If a system is not complete, then it is consistent." Seeing that complete usually means "proves $\sigma$ or $\lnot\sigma$ for every sentence $\sigma$" and that consistent usually means "does not prove every sentence $\sigma$," a system that is not complete must be consistent. There are variations but, in any case, I don't think your second sentence exactly says what you meant to say. Aug14 awarded Quorum Aug6 comment Axiom of choice - to use or not to use Also, the axiom of choice is not necessarily non-constructive. For example, full choice is valid in constructive type theory. Aug3 awarded Revival Aug3 comment Proving that the set of algebraic numbers is countable without AC And yes, countable means $\leq \aleph_0$ and, in particular, infinite Dedekind finite sets are "uncountable" in ZF. So one shouldn't think that "uncountable" means "large" in ZF...