Can Peano arithmetic define the set of base 10 palindromic numbers?

Question

A base 10 palindrome is a number that when written in base 10 and the digits are reversed, gives the same number. I am wondering, can Peano arithmetic define the set of base 10 palindromes? I don't even need to be given an explicit definition, merely a proof that that set is definable in the language of Peano Arithmetic. An explicit definition of that set, using abbreviations if necessary, would be a bonus.

Answer 1

Yes. Peano arithmetic can be used to define any primitive recursive function. Checking whether a number is a base 10 palindrome can be done with a primitive recursive function. Therefore, Peano arithmetic can define a base 10 palindrome.