All Questions
4 questions
15
votes
5
answers
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In what sense does the sentence $\operatorname{con}(\mathsf{PA})$ "say" that $\mathsf{PA}$ is consistent?
It seems common amongst logicians to think of "truth" as being relative to a particular structure. Consider, for instance, the first-order theory of groups. The sentence $\forall x\forall y(...
- 961
5
votes
1
answer
485
views
Extensions of the Ackermann interpretation to nonstandard theories of arithmetic
In their paper, " On Interpretations of Arithmetic and Set Theory" (Notre Dame Journal of Formal Logic, Vol. 8, No. 4 (2007), pp. 497-510) in section 7, "Fragments of Arithmetic and Set ...
- 6,132
6
votes
1
answer
209
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Is $PRA$ + $TI({\epsilon_0})$ mutually interpretable with some theory in the language of set theory?
As is well known, the following theory is equiconsistent with $PA$:
$ZFC$ with the axiom of infinity replaced by its negation.
Since this theory is equiconsistent with $PA$, it would seem ...
- 6,132
19
votes
3
answers
2k
views
Is platonism regarding arithmetic consistent with the multiverse view in set theory?
A "truth" platonist for arithmetic believes, given a statement in the language of arithmetic, that the problem whether the statement is true has a definite answer.
Prof. Hamkins has argued for a ...
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