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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 Best Mathematical Logic Books the Style of Which is Like a Mathematics Publication rather than a Logic Publication?
@Comeseeconquer: I am afraid I have the same troubles than Carl to follow your question. How do you think it is written "for every $x$, if $x$ is a real number then $x^2 \geq 0$" in a mathematical book?
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 )
Apr
11
comment The idea of “generators” for arbitrary categories
I am not able to understand what you mean with "$\{ x \circ f \mid x \in X \}$"; can you tell me what is $f$?
Apr
11
comment The idea of “generators” for arbitrary categories
@espen180: Be careful because the upset generated is not the same thing than the filter generated. The notion of filter is isually used in the context of lattices (a particular kind of partial orders), and filters are always closed under finite meets, while upsets might not be closed under finite meets.
Apr
11
comment The idea of “generators” for arbitrary categories
@Mariano: I am afraid that this wikipedia notion does not coincide with the one I have written above for partial orders (although the same word "generator" is used), so it is not adequate for what I really want to generalize.
Mar
28
comment nonisomorphic graph drawings
You can try to use some software for drawing them, this is always helpful (see for instance the "sage" code in the question ask.sagemath.org/question/3473/… )
Mar
28
comment How to explain the power of PA to non-logicians
This essentially means that all $\Sigma_1$-setences that are true in the standard model are provable in PA. This result can be find in most of logic books dealing with PA (and Robinson's Q). In particular, you can take a look at the notes by Peter Smith logicmatters.net/igt/godel-without-tears (in the current version is Theorem 17 in Episode 5, page 40)
Mar
28
comment How to explain the power of PA to non-logicians
Do you consider the fact that "PA (indeed Robinson Q is enough) is $\Sigma_1$-complete" strong enough?
Mar
27
comment Mathematical intro to Turing machines
One example is the following "classic" written by Martin Davis amazon.com/Computability-Unsolvability-Prof-Martin-Davis/dp/…
Mar
19
comment Show that a recursively inseparable pair of recursively enumerable sets exists
Yes, there is a standard proof (for two sets whose definiton only involves Turing machines). One place where you can find this is in Theorem 3.3.5 of the wonderful notes "Syllabus Computability Theory" written by Sebastiaan A. Terwijn math.ru.nl/~terwijn/teaching.html After you know these two sets are inseparable you can easily prove the inseparability of sets with a "logic" flavour (like in Biderman answer)
Mar
18
comment Books (and supporting material) that are useful in deconstructing one's intuition?
@Sabysachi: torus solution?