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Results tagged with lo.logic
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user 41947
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.
22
votes
Accepted
The symmetric group theory of natural numbers
It's possible to embed within the theory of the permutation group $S_n$ the theory of second-order arithmetic for numbers between $0$ and $n-1$. Using this we can construct propositions corresponding …
- 1,105
6
votes
Checkmate in $\omega$ moves?
I have an idea for how to get up to $\omega_1^{CK}$. Consider this position: black's king is trapped and white has a mate in one. However, white's king is trapped in a perpetual check. The only way ou …
- 1,105
6
votes
3
answers
599
views
Do "seemingly impossible functional programs" work with arrow types interpreted as Turing ma...
The title is a reference to this article by Martin Escardo, referring to work by originally by Ulrich Berger. It occurred that the programs described in this article can interpreted in the Turing mach …
- 1,105
2
votes
Constructively, is the unit of the “free abelian group” monad on sets injective?
Here's yet another construction of the free abelian group on an arbitrary set, and a proof of the claim. I haven't seen the proof in Mines, Richman, Ruitenburg so I don't know how similar this is to t …
- 1,105
1
vote
Provability in $S^1_2$
(Note: I'm not actually familiar with $S^1_2$ and the related formalism, but I'm going by your description of the theory, and I have been already thinking about related questions in an informal way.)
…
- 1,105