I tiakina i:
| Kaituhi matua: | |
|---|---|
| Hōputu: | Preprint |
| I whakaputaina: |
2011
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| Ngā marau: | |
| Urunga tuihono: | https://arxiv.org/abs/1105.0321 |
| Ngā Tūtohu: |
Tāpirihia he Tūtohu
Kāore He Tūtohu, Me noho koe te mea tuatahi ki te tūtohu i tēnei pūkete!
|
Rārangi ihirangi:
- The standard interpretation of first-order number theory (PA), according to the generally accepted view, associates well-defined set-theoretic entities with each and every well-formed formula of this system. But this implies that the class of PA theorems is semantically defined by a class sign of PA itself, (E x_2) Pf(x_2, x_1), in the following sense: with b' the PA numeral for the number b, (E x_2) Pf(x_2, b') is true under the standard interpretation if and only if b is the Godel number of a PA theorem. From this however it is easily established, by a modification of Godel's proof, that the class of PA theorems, and hence the standard interpretation of PA itself, is not well defined after all.