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Results tagged with lo.logic
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user 2693
first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
7
votes
The sets in mathematical logic
There are a few problems you seem to be having. First of all, the statement "mathematical logic depends on ZFC" doesn't make sense.
As mathematical logicians, when we study formal systems, we should …
- 464
26
votes
3
answers
6k
views
Presburger Arithmetic
Presburger arithmetic apparently proves its own consistency. Does anyone have a reference to an exposition of this? It's not clear to me how to encode the statement "Presburger arithmetic is consisten …
- 464
10
votes
Accepted
Why is every finite set Diophantine?
Or, very simply stated, given the finite set $S = \{a_1, \dots , a_k\}$, consider the diophantine equation: $$(n-a_1)\dots(n-a_k)=0.$$
EDIT: Then we can write S as $\{ \ n \ | \ \exists x : (n-a_1)\do …
- 464
5
votes
The best text to study both incompleteness theorems
Peter Smith's book is great. It's very readable and contains all the details. The problem is that it doesn't leave anything for you to do! If you want to get your hands dirty and work a few things out …
1
vote
Propositional logic and first order logic textbook
As a clear introduction to propositional and first order logic for the mathematically minded, I think Logic and Structure by Van Dalen is in a class of its own. The majority of the book is not particu …