9
votes
3answers
138 views

The category of theorems and proofs

On a philosophy website, it said that you could have a category with theorems as objects and proofs as arrows. This sounds awesome, but I couldn't find anything on the web that has both "category" and ...
4
votes
2answers
84 views

Graph that represents logical reasoning

The proof of a statement $X$ in terms of assumptions $A$, $B$ and $C$ can sometimes be represented using a directed graph: $$ \begin{matrix} & & X\\ & \nearrow & & ...
3
votes
1answer
68 views

Intuitionistic Linear Logic

I am currently going through some papers that use the "intuitionistic version" of Girard's Linear Logic. Problem is, i seem to find very little literature on it. There is a lot done on Linear Logic ...
1
vote
1answer
39 views

Introduction to functional interpretations

Any good recomendations for an introduction to functional interpretations? I understand this is a little vague but i haven't had much contact with the area. I am particularly interested in the ...
0
votes
1answer
54 views

Help with positive- and negative-forms in Proof Theory

I need help in understanding a device used bu Kurt Schütte, Proof Theory (1977). In treating classical sentential calculus, he use - in place of truth-tables - the device of positive- and ...
0
votes
2answers
171 views

What are some good introductory books on mathematical proofs?

There was a time when I avoided math proofs, but now I am starting to enjoy them. I am taking Intro to Linear Algebra and am falling in love with proofs. Are there any introduction to mathematical ...
4
votes
5answers
570 views

Books on logic, proof theory and set theory?

I graduated in Computer Science at University of Bologna in Italy some years ago. For various reasons now I am discovering a back interest in mathematic logic higher than I was a student. I have only ...
3
votes
2answers
212 views

Goodstein's theorem without transfinite induction

Is it possible to prove Goodstein's theorem without transfinite induction? Is there such a proof?
7
votes
1answer
132 views

Learning how to prove that a function can't proved total?

In proof-theory one can prove that in, say, Peano Arithmetic one can't prove a function $f$ total. Often this seems to mean $f$ is growing too fast to be provably total. I have some background in ...
5
votes
5answers
325 views

Can we decide a conjecture is decidable without knowing a conjecture is correct or false?

Can we decide a conjecture is decidable without knowing a conjecture is correct or false? I asked this question because I assume that the millenium prize problem is already to be decidable, otherwise ...