Tagged Questions

7
votes
4answers
137 views

Books in foundations of mathematical logic

I'm a civil engineer that spends all of its free time (with the permission of my wife and my two children) studying set theory and mathematical logic. For instance, I've read and enjoyed "Axiomatic ...
3
votes
2answers
77 views

Goodstein's theorem without transfinite induction

Is it possible to prove Goodstein's theorem without transfinite induction? Is there such a proof?
2
votes
1answer
50 views

Logic about systems?

In Godel's Incompleteness Theorem, his theorem is about a system of logic. Where can I find more about this study, especially the notation? EDIT I mean logic about systems in general. I worded the ...
5
votes
1answer
60 views

Tarski's Undefinability Theorem Reference

There are many books articles that look to explain Godel's Incompleteness Theorems for laymen. Does anyone know of some good material (free online is most appreciated) that attempts to do the same ...
5
votes
2answers
103 views

Overview and introduction to strong logics

Is there a nice and simple paper which summarizes the definitions and properties of strong logics? When I say strong logics I mean something like stationary logic, or Magidor-Malitz quantifier, $\cal ...
2
votes
1answer
67 views

Earliest proof of completeness for axiomatization of Boolean Algebra

Suppose we define Boolean algebra as the system of algebraic rules (logical equivalences) obeyed by AND, OR, NOT with AND, OR, NOT defined by the usual truth tables. We also have variables, which can ...
0
votes
2answers
117 views

Inhabited versus nonempty sets - disasters without excluded middle?

The attached screenshot, from Goldblatt's Topoi, shows at a glance the distinction between the constructive concept of inhabited set versus that of the classical nonempty set. These definitions ...
8
votes
4answers
187 views

The Maths necessary to understand Logic, Model theory and Set theory to a very high level

I am studying Philosophy but most of my interests have to do with the philosophy of Maths and Logic. I would like to be able to have a very high level of competence in the topics mentioned in the ...
1
vote
1answer
86 views

Recommendation for a logic book to understand Godel's theorem

I have studied set theory but I couldn't understand even the first line of the Godel's proof. For instance, $\omega^n$ means the set of functions from $\omega$ to $n$ in my set theory, ZFC, but the ...
3
votes
2answers
153 views

Which are “big theorems” of descriptive set theory?

Question: If one were to fully understand 10 theorems in DST, or 15,20,25,30 theorems, which ones would be the most important to understand in order to work towards an understanding of descriptive set ...
1
vote
1answer
110 views

reference recommendation on mathematical logics

It is a bit of strange that I haven't be trained on such a topic. It wouldn't influence my daily work but I would like to study some materials on my own. So, dear fellows, you got any classic ref in ...
3
votes
1answer
114 views

Reference request for examples of probabilistic heuristics, help put some examples in a broader context.

I was thinking about how probability is used in heuristic arguments, an example being the argument that there are an infinite number of twin primes: the probability that $n$ is the first of two twin ...
3
votes
0answers
81 views

Cutest proof that PA proves its finitely axiomatised subtheories are consistent?

Back in 1952, Mostowski proved that PA proves the consistency of its finitely axiomatised sub-theories. Any pointers to particularly nice later proofs of this lovely result? Or indeed particular nice ...
7
votes
1answer
96 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
3answers
245 views

All real functions are continuous

I've heard that within the field of intuitionistic mathematics, all real functions are continuous (i.e. there are no discontinuous functions). Is there a good book where I can find a proof of this ...

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