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 Feb 2 comment Linear Algebra book for beginners I suggest you the online version of a "A First Course in Linear Algebra" by Robert A. Beezer. It is avaiable from linear.ups.edu/download.html and what it is really great is the possibility to use the (free) software "sage" for the examples. Jan 15 comment “Minimal upper bounds” in a categorical setting @Eric: That was one of my attempts, but in this case it happens that corproducts do not satisfy this "minimality" (if I am not worng). Jan 15 comment “Minimal upper bounds” in a categorical setting @Eric: I am asking for a categorical notion of "a minimal upper bound" as oposed to "the minimum upper bound". In particular, the unicity (up to isomorphism) needs to be lost. Jan 6 comment Number of k-ary monotone maps from 1..n+1 to 1..n+1. @Random: Thanks. As you have pointed out, Dedekind numbers provide an answer for the case n=1. Jan 6 comment Number of k-ary monotone maps from 1..n+1 to 1..n+1. @Brian: See the clarification I have added to the question. Jan 4 comment Finite Strong Completeness Theorem for BL logic Hint: When you assume that $\varphi_1, \ldots, \varphi_n \not \vdash_{BL} \varphi$, use the fact that $\vdash_{BL}$ is strongly complete with respect to the class of all BL-chains. I guess you are aware of this result (it can be "easily" proved using a Lindenbaum-Tarski argument together with the fact that all subdirectly irreducible BL-algebras are chains). Jan 4 comment Finite Strong Completeness Theorem for BL logic What are the problems you find when you try to use any of these two embeddability results to provide a direct proof (of the finite strong completeness)? Dec 31 comment Graded modules/algebras on commutative monoids? What is the definition of "M-graded abelian group"? Any reference? I wasn't able to find it in a quick google search Sep 5 comment Is there an algorithm for computing pushouts in $\sf FinSet$? Two issues: 1) Which environment category are you considering (sets with total functions, finite sets with total functions, etc)? 2) If you know how to calculate coproducts and coequalizers then there is a well known method explaining how to calculate pushouts (and indeed all colimits); a good summary of the method is given in mathoverflow.net/questions/171920/… Jul 17 comment What is the Best Introduction to Dedekind Cuts? Why not "Continuity and Irrational Numbers" by Richard Dedekind? It is freely available from gutenberg.org/ebooks/21016 and I am pretty sure you will not find it very demanding. May 17 comment MTL algebra 'prelinearity' condition etymology @user: The generation is done in the usual way of universal algebra, which is the HSP theorem. Take a look at en.wikipedia.org/wiki/Universal_algebra#Some_basic_theorems May 16 comment MTL algebra 'prelinearity' condition etymology In partial orders, the word "linear" is also used as a synonym of being a total order (i.e., a chain). This is the appropiate sense to understand prelinearity in the MTL setting; the reason is that the variety of MTL algebras (i.e., prelinear FLew algebras) is generated by chains. To sum up, no realtionship with the use of the word "linear" in "Linear Algebras" Mar 5 comment What technical books should I read to understand clearly Gödel's theorems and their implications for math? I also suggest the lecture notes "Gödel Without (Too Many) Tears" by the very Peter Smith. They are available from logicmatters.net/igt/godel-without-tears Feb 18 comment Reference for Algebraic Categories Look at the book "Algebraic Theories: A Categorical Introduction to General Algebra" by Adamek et al. books.google.es/books?id=siNlAn8Bm30C The book is available from Adamek's web page iti.cs.tu-bs.de/~adamek/algebraic_theories.pdf Jan 19 comment When do finite linear orders have the same theory in MSO? Hint: Combine the following two facts to answer your question 1) finite structures have the same first-order theory iff they are isomorphic, 2) the monadic second order language is more expressive than the first-order one. Jan 12 comment Fuzzy Logic Question Help Hint: First, think about how solving it with classical logic. And then use the same idea. Oct 8 comment Colimits in the 2-category of partial functions (which is locally posetal) @Zhen: Why is this true? Given a plain bicomplete category $\mathcal{C}$, there are many ways to look at it as a locally posetal one. Thus, I can imagine it might be the case there is some strange partial order where bicolimits do not exist (while colimits, as a plain category, exist). Is this not possible? Sep 7 comment Any Computational Number Theory Book, include software programs for key steps of the proofs of major theorem? Something close (except for what Conifold has said in his comment) can be found in the book "Elementary Number Theory: Primes, Congruences, and Secrets" by William Stein. The book and the software are freely availabe: visit wstein.org/ent and sagemath.org Sep 2 comment Colimits in the category of “sets with partial mappings” Thanks for the clarification. I guess you mean "colimits" (since limits are not preserved). May 30 comment How did Kurt Gödel's Incompleteness Theorem affect the mathematical world? To start take a look at the papers published in this volume of the Notices AMS ams.org/notices/200604 (in particular I point out the paper by Solomon Feferman). Another related paper worth looking at it is one by Macintyre (take a look at books.google.es/books?id=Tg0WXU5_8EgC&pg=PA3 )