Reputation
759
Top tag
Next privilege 1,000 Rep.
Create new tags
Badges
4 11
Newest
 Curious
Impact
~31k people reached

  • 0 posts edited
  • 0 helpful flags
  • 91 votes cast
Mar
31
revised Need help locating a paper
deleted 4 characters in body
Mar
31
answered Need help locating a paper
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?
Mar
15
comment Book on the first-order modal logic
@user132181: The standard translation only works for propositional modal logic (and it translates these formulas into first-order, non-modal, formulas). Thus, right now I am afraid that your question does not make sense: could you clarify your question?
Mar
13
comment When is a Decidable Set Decidable?
I suspect Russell is confusing two different uses of the term "undecidable". We have "undecidability in a formal theory" which applies to a sentence and refers to its unprovability. And then we also have "undecidability in a computability setting" which applies to a family (set) of finite objects and refers to the fact that this set cannot be computed by a Turing machine. For this second use there are some people which have advocated for using the word "uncomputable" instead of "undecidable", in order to avoid these misunderstandings.
Feb
15
comment Complexity of Recursively Inseparable Sets
@Easterly: What do you mean here with the word "Complexity"?
Jan
31
answered Famous Math Texts in Spanish?
Jan
20
answered List naturals in ascending product order
Jan
10
awarded  Yearling
Jan
10
comment Why are mathematical proofs that rely on computers controversial?
@DumpsterDoofus (and the upvoters): What is the statement you talk about?
Jan
5
comment Determining if a theory in first-order logic is decidable
@Sid: Use the "informal proof" given by André. In the proof it is crucial that you know that your theory is complete. Indeed, for complete theories (but not in general) it is known that "decidable" coincides with "recursively axiomatizable".
Dec
22
comment Good textbook on geometries
And the recent "trilogy" by Borceux. I think up to now only the first two volumes have been published: amazon.com/An-Axiomatic-Approach-Geometry-Geometric/dp/… amazon.com/An-Algebraic-Approach-Geometry-Geometric/dp/…
Nov
10
answered Books about Turing machines and undecidability
Oct
28
comment Why does undecidability of arithmetic not follow from that of first-order logic?
Indeed, it is also well known that these two sets (arithmetic truths versus firs-order validities) have different Turing (undecidability) degrees. In particular, there is no computable reduction reducing "arithemtic truths" to "first-order validities". If you want to take a deeper look at this I suggest you start looking at the artihmetical hierarchy (for instance, at wikipedia en.wikipedia.org/wiki/Arithmetical_hierarchy )
Aug
27
comment Does ZFC pin down precisely which theorems PA can and cannot prove?
This comment develops (just a bit) Carl's comment. It is easy to prove from the assumption that "for all sentences $\phi$ in the language of PA, it holds that either $ZFC \vdash (PA \vdash \phi)$ or $ZFC \vdash (PA \not \vdash \phi)$" (together with assuming that $ZFC$ is consistent) that there is an algorithm to compute "provability in PA". The algorithm is the trivial one you expect (use provability in ZFC until you find the proof that shows ...). Using the well-known fact that PA is non-computable one concludes that the answer to your question is NO.