The tag has no wiki summary.

learn more… | top users | synonyms

12
votes
1answer
419 views

Is there a nonstandard model of arithmetic having precisely one inductive truth predicate?

$\newcommand\Tr{\text{Tr}}$My question is whether there can be a nonstandard model of PA having a unique inductive truth predicate. Background. If $\mathcal{N}=\langle N,+,\cdot,0,1,<\rangle$ is ...
14
votes
5answers
767 views

What is the spectrum of possible cofinality types for cuts in an ordered field? Or in a model of the hyperreals? Or in a nonstandard model of arithmetic?

I am interested to know the full range of possibilities for the cofinality type of cuts in an ordered field and in other structures, such as nonstandard models of arithmetic. Definitions. ...
6
votes
1answer
564 views

Nonstandard models of PA of large cardinal size

It is easy to overlook the fact that the existence of a given large cardinal provides us with a true arithmetical statement that would otherwise be false if the large cardinal notion were not ...