Before revision: First-order theories of real closed fields typically cannot express the notion " is a natural number".Since theories of real closed fields axiomatise the constants and , and the operations of addition and multiplication, a theory which could additionally express " is a natural number" would be incomplete due to Gödel's incompleteness theorems.
After revision: In real closed fieldsFirst-order theories of real closed fields typically cannot express the notion " is a natural number".Since theories of real closed fields axiomatise the constants and , and the operations of addition and multiplication, a theory which could additionally express " is a natural number" would be incomplete due to Gödel's incompleteness theorems.