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Results tagged with lo.logic
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user 3206
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.
5
votes
Accepted
The existence of an algebra whose set of identities and first order theory are equivalent
I imagine that definitions of $Mod, Th, Var$ and so on have not changed since I saw them decades ago. The trivial one element algebra in any finite type (and likely any infinite type) is an easy exam …
- 3,209
5
votes
What are the most attractive Turing undecidable problems in mathematics?
Let a finite structure be a finite underlying set A
along with a finite set of finitary operation from A to
itself. Such creatures are called algebras in the
study of universal algebra, and one su …
4
votes
What do you do if you believe a problem is undecidable?
Joel David Hamkins has given a good answer in the case of (2), where a certain notion when expressed formally in the language of a theory $T$ (and also the negation of this notion) may not be provable …
- 3,209
2
votes
Using the multiverse approach to decide the law of the exluded middle?
I offer a different perspective on the question, which I hope will be found
useful.
One view of logic is strongly syntactic: develop a language, and develop
rules for manipulating this language and …
- 3,209
0
votes
Strong induction without a base case
I posted an answer on sci.math.research recently where I used induction with a base case, and then thought I could use strong induction instead. Later another poster came up with a nice argument that …