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Results tagged with definability
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user 6794
definability by formulas in first-order logic, e.g. as explained at https://en.wikipedia.org/wiki/Definable_set, or as in J. Robinson's first-order definition of the integers in the field of rationals
9
votes
Accepted
What ordinals are definable relations in Peano Arithmetic?
These are the recursive ordinals. The same well-order-types can be realized by recursive relations as by hyperarithmetical relations. PA-definable, i.e., arithmetical, falls nicely between these two. …
- 73.1k
6
votes
Accepted
Reconstructing a model from its definable sets
The answer to the first part of #2 is no. In a language with (just) one binary relation, let the two models be $\omega$ with the relation interpreted as $<$ in one model and as $>$ in the other.
For …
- 73.1k
4
votes
Accepted
Definability of arithmetic functions and relations
The set of natural numbers, when equipped with just the operation of multiplication, has lots of automorphisms, induced by arbitrary permutations of the primes. These generally don't preserve addition …
- 73.1k