Tagged Questions

92 views

reference on aperiodicity and cluster [closed]

From this image: I believe there is a message relating those clusters drawn in picture and aperiodic tiling. Does anyone have some reference on this? Thank you :)
639 views

Salvaging Leibnizian formalism?

Can one justify Leibniz's formalism in a suitable algebraic or topological context? We have published some papers recently where we argue that Leibniz's formalism for the calculus wasn't ...
128 views

Countable model theory for $\omega$-stable theories?

This is a bit of a fishing expedition, because I'm not sure what I'm looking for. Very vaguely stated, here's the driving question: What conditions on an $\omega$-stable theory make the class of ...
90 views

topological space of Wang Tile

When trying to reprove a theorem in Wang tile: An established proof in Wang Tile which I doubt , a few notions are provided which I would like to seek for more information: For a given set of blocks ...
802 views

Why can't mathematics be formalised in terms of classes rather than sets? [closed]

I've always been curious about the seeming compulsion to found mathematics upon sets, be it ZF(C) or some other system. Of course, there are other approaches these days like category theory and type ...
1k views

Does formalizing math require search and creativity, or is it near-mechanical?

I remember reading somewhere that it takes about a week to convert a page of math into something a proof-assistant like Isabelle or HOL Light would accept. Is this type of conversion something that ...
119 views

characterization of all periodic tiling of a simple set of Wang Tile

Consider a set of Wang Tile such that all the edges are either 1 or 0.... there are 16 elements in such a set. Now, I wish to characterize all the periodic tilings of this set (better if they are ...
122 views

Basis of periodic tiling of Wang tile

Given a set of Wang tile, Given 3 periodic tiling: A, B, C We define 3 vector F[A], F[B], F[C] each vector correspond to the appearing frequency of each type of tiles in the tiling. Now, we ...
90 views

We know that any closed cycle of a graph could be decomposed into sum of simple cycles. To translate this theorem into tiling of 1D (Wang tile). We know that any 1D periodic tiling could be ...
331 views

Is there a theory of abuse of notation? [closed]

Is there any theory about the different ways notation can be abused and which abuses are ineliminable without complicating the notation in some essential way? We can define "abuse of notation" as any ...
1k views

Is Turing degree actually useful in real life? [closed]

In theoretical computer science, we classify problems according to their Turing degree. Is there any practical application of this? Edit: Given that we cannot explicitly and mechanically understand ...
973 views

What is the definition of a large cardinal axiom?

In different books one can find different implicit definitions for a large cardinal axiom. My question is that which one of these definitions are more popular or standard amongst set theorists? Any ...
196 views

Natural $\Pi^1_2$ (or worse) classes of structures?

(To clarify, my interest is mainly lightface, that is, $\Pi^1_2$ instead of $\bf \Pi^1_2$, although it doesn't particularly matter.) This is just an idle curiosity. In logic, I find myself frequently ...
421 views

Hilbert style axiomatic proof or sequent Calculus?

I am puzzling with the question which of the two proof systems (Hilbert style axiomatic proofs or substructural Sequent Calculi) is the most discriminatory? With discriminatory I mean is which proof ...
621 views

What are current trends/questions in algebraic logic?

What are current trends/questions in algebraic logic? I mean the research developed by Paul Halmos. Could anyone give some references for the overview of its history? Any overview of its application ...
1k views

Intuitionistic logic as quantization of classical logic?

A classically trained mathematician is more likely to be familiar (at least anecdotally) with an area of mathematical physics such as deformation quantization than with Intuitionistic logic. It is ...
1k views

Euler's mathematics in terms of modern theories?

Some aspects of Euler's work were formalized in terms of modern infinitesimal theories by Laugwitz, McKinzie, Tuckey, and others. Referring to the latter, G. Ferraro claims that "one can see in ...
1k views

Self-containing structures

(This question is partly inspired by What is inter-universal geometry?.) I have absolutely no background in Teichmuller theory or any related subject, but what I can follow of Mochizuki's description ...
414 views

New research on coding in reverse mathematics?

Coding is obviously a fundamental tool in reverse mathematics, and practitioners take care to both demonstrate the correctness of their coding mechanisms and point out their limitations. Harvey ...
578 views

Mendelson's *Mathematical Logic* and the missing Appendix on the consistency of PA

A very soft question, but I hope not out of order here. In the first edition of Elliott Mendelson's classic Introduction to Mathematical Logic (1964) there is an appendix, giving a version of ...
705 views

In the first semester of 2012 I took a course in General Topology and Set Theory, at undergraduate level. For topology, I was instructed to use Engelking's General Topology; albeit I had a great ...
2k views

Excellent uses of induction and recursion

Can you make an example of a great proof by induction or construction by recursion? Given that you already have your own idea of what "great" means, here it can also be taken to mean that the chosen ...