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Apr
17
comment Maximality statements that cannot be proved using $\mathsf{ZL}$
"existence of ultrafilters" (or BPI) is an answer to the question in the title, but not to the actual question.
Apr
10
awarded  Nice Answer
Apr
9
revised How do I apply the Boolean Prime Ideal Theorem?
minor modifications: typos. variables are generators.
Apr
9
comment How do I apply the Boolean Prime Ideal Theorem?
It seems that I was half a minute faster...
Apr
9
answered How do I apply the Boolean Prime Ideal Theorem?
Apr
9
answered recursive equation to solve( similar to combinatorics)
Apr
8
comment What are some examples of narrowly missed discoveries in the history of mathematics?
Cantor not only discovered and rigorously defined the idea of equinumerosity of infinite sets, he also gave an explicit example of two infinite set of distinct cardinalities. I do not see anything like that in Galileo's argument.
Apr
3
revised Is a sigma-finite Borel measure over $\mathbb R$ determined by its values on the continuous functions?
typo: ies -> lies
Mar
31
comment Mathematicians wearing hats on arbitrary total orders
You don't say this explicitly, but I assume that each mathematician knows his place in the total order, right?
Mar
30
comment Notions of infinity in $\mathsf{ZF}$ without choice
(2) is strictly stronger than (1), but equivalent to the dual version of (1) ("1-1 map from $X$ into $X\setminus \{x_0\}$"). The dual version of (2), on the other hand (surjection from $X$ onto $\omega$) follows from (1) but is strictly weaker
Mar
30
comment Proof that no differentiable space-filling curve exists
A great theorem! But only a "Peano type function", not really a curve, since neither $f_1$ nor $f_2$ is continuous.
Mar
30
answered The automorphism groups of smallest grammars of a language string are isomorphic
Mar
29
comment The automorphism groups of smallest grammars of a language string are isomorphic
(4) If I apply the permutation to the right hand sides of your grammar, I get $A\to BB$, $B\to ba$, which generates a different string.
Mar
29
comment The automorphism groups of smallest grammars of a language string are isomorphic
(1) Do you mean: Whenever we have two smallest grammars computing the same string, their automorphism groups are isomorphic? (2) On which set does the automorphism group of a grammar act if the RHSs have different lengths? (3) What do you mean by "smallest"? The smallest number of rules, the smallest number of nonterminals, the smallest number of symbols, including or not including arrows and/or commas, etc?
Mar
28
comment Connectedness in the language of path-connectedness
A more interesting follow-up question would be: Given $\kappa$, is there a not too large space (say: of weight $\kappa$, or perhaps cardinality or density $\kappa$, or perhaps we might allow $\kappa^+$ or $2^\kappa$?) which decides connectedness (in the way suggested by Dominic) for all small spaces (or weight or cardinality or density $\le \kappa$)?
Mar
27
revised Continuous image relation on topological spaces
non-Hausdorff is the main point, not "finite".
Mar
26
comment Freiling's Axiom of Symmetry Concretized
To prove "my" version from "your" version, just apply "your" version to the function $g(x):= f(x) \setminus \{x\}$.
Mar
26
comment Freiling's Axiom of Symmetry Concretized
If you demand that $x\notin f(x)$ for all $x$, then the free set $F$ will have the property $y\notin f(z)$ for all $y,z\in F$. If you do not demand this, you get $y\notin f(z)$ only for all distinct $y,z\in F$.
Mar
25
answered Freiling's Axiom of Symmetry Concretized
Mar
25
answered Continuous image relation on topological spaces