# user18921

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 7h comment How many ways can we totally order a set $X$ (but not necessarily the whole set $X$, perhaps just a subset) up to isomorphism? @AndresCaicedo, okay I'll have a think about it. Probably just end up asking another question at some point. 9h comment How many ways can we totally order a set $X$ (but not necessarily the whole set $X$, perhaps just a subset) up to isomorphism? @AndresCaicedo, hey any idea what the answer is for scattered linear orderings? 22h comment How many ways can we totally order a set $X$ (but not necessarily the whole set $X$, perhaps just a subset) up to isomorphism? @AndresCaicedo, thanks. I get it now. 23h asked How many ways can we totally order a set $X$ (but not necessarily the whole set $X$, perhaps just a subset) up to isomorphism? 1d accepted Is there always a bijection between a universe of set theory and its ordinal numbers? 1d comment How to prove that for finite, nonempty sets $A,B$ $|A \times B| = |A|\cdot|B|$ Pretty sure that is the definition of $|A|\cdot|B|$. You just need to check that the definition is well-defined. i.e. Basically, just assume you have three sets $A,A',B$ and a bijection $f : A \rightarrow A',$ and produce a bijection $A \times B \rightarrow A' \times B$. Then just say that "the corresponding argument for $B$ is similar." 1d asked General question: what happens if we replace the regularity stipulation in GCH with other conditions? 2d comment Is it possible that “A counter-example exists but it cannot be found” @TrevorWilson, I'm not sure I follow, so let me take a look at Hamkin's stuff and I'll get back to you. 2d comment Is it possible that “A counter-example exists but it cannot be found” @TrevorWilson, surely we should be considering models of second-order set theory, i.e. $\mathrm{ZFC2}$ for this question. Otherwise, the model's real line needn't be the true real line relative to the ambient universe. 2d comment Arbitrary (i.e. not necessarily finite-dimensional) vector spaces; reference request. @AsafKaragila, not really sure man, I was just under the impression that a lot of linear algebra falls apart. Probably, this impression is baseless, 2d accepted Confusion about cofinality 2d comment Arbitrary (i.e. not necessarily finite-dimensional) vector spaces; reference request. Thanks for the info, +1. 2d asked Arbitrary (i.e. not necessarily finite-dimensional) vector spaces; reference request. Apr14 accepted When solving a DE, what should our premises be? Apr14 comment Modern book on Gödel's incompleteness theorems in all technical details Peter Smith's Introduction to Godel's Theorems is a readable introduction that includes the sort of technical details you seem to be interested in; however if you want "each and every technical aspect" it may not be sufficient. At the very least, its a good place to start. Apr14 comment Converting statements with term 'only' and 'any' to predicate logic "Only dogs are mammals" becomes "every mammal is a dog." Apr14 revised Is there a traditional name for the “eigenspace” function? added 1 characters in body Apr14 comment Is there a traditional name for the “eigenspace” function? @lhf, thanks. $\;\!$ Apr14 comment Is there a traditional name for the “eigenspace” function? @lhf, its very hard to learn more about a function if you do not know its name. Apr14 revised Is there a traditional name for the “eigenspace” function? deleted 5 characters in body