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Aug
28
revised Coloring graph such that the coloring classes are not maximal independent sets
added 95 characters in body
Aug
28
answered Coloring graph such that the coloring classes are not maximal independent sets
Aug
23
comment Who defined and who coined “module”?
That 1927 Monthly article is also the online OED's earlist citation for this sense of "module".
Aug
22
revised When does a hypergraph represent maximal independent sets?
added 7 characters in body
Aug
22
answered When does a hypergraph represent maximal independent sets?
Aug
20
comment Is any axiom system for sets categorical?
But a countable model of set theory can be characterized up to isomorphism by a single first-order sentence of infinite length, right?
Jul
31
comment Proofs of the uncountability of the reals.
Wouldn't it be simpler to work with surjections instead of injections? There is a surjection from $\mathcal P(\omega)$ to $\omega_1$, there is no surjection from $\omega$ to $\omega_1$, therefore $\mathcal P(\omega)$ is uncountable.
Jul
16
answered Is quasivariety generated by all perfect graphs finitely axiomatizable?
Jul
16
comment Is quasivariety generated by all perfect graphs finitely axiomatizable?
If the class is axiomatizable by universal Horn sentences, and if it's finitely axiomatizable, then it's finitely axiomatizable by Horn sentences; this follows from the compactness theorem. However, the class of perfect graphs is not closed under direct product. Let $G$ be the graph obtained by adding one more edge to the cycle $C_5$.Then $G$ is perfect, but the direct product $G\times G$ is easily seen to contain $C_5$ as an induced subgraph. so it's not perfect. Many different products of graphs are considered in graph theory; maybe the theorem you cited is about some other graph product?
Jul
15
revised Does the symmetric group on an infinite set have a minimal generating set?
added 209 characters in body
Jul
15
revised Removal of non-isomorphic edges results in the same graph
corrected grammar
Jul
15
suggested suggested edit on Removal of non-isomorphic edges results in the same graph
Jul
11
awarded  Nice Answer
Jul
11
revised Does the symmetric group on an infinite set have a minimal generating set?
added 432 characters in body
Jul
11
revised Does the symmetric group on an infinite set have a minimal generating set?
added 1 character in body
Jul
11
revised Does the symmetric group on an infinite set have a minimal generating set?
added 3 characters in body
Jul
11
revised Does the symmetric group on an infinite set have a minimal generating set?
corrected a typo
Jul
11
comment Does the symmetric group on an infinite set have a minimal generating set?
@TheMaskedAvenger You may be right; I'm a newbie here and don't know much about the rules and culture of this site. I posted this with the idea that Jeremy Rickard might want to incorporate the argument into his answer to make it self-contained.
Jul
11
comment Does the symmetric group on an infinite set have a minimal generating set?
@JeremyRickard I've copied out the proof of Galvin's Theorem 3.1 from a reprint of his paper, and posted it as a comment-disguised-as-an-answer. Hope I didn't make too many typos.
Jul
11
answered Does the symmetric group on an infinite set have a minimal generating set?