If you have only + in your logic, you do not get the Gödel curse: the full first order fragment, called Presburger Arithmetic is decidable and complete.
But you're juuuust squeezing by! It turns out this innocent looking theory is quite expressive, and this expressiveness comes with a baby version of the incompleteness theorems: a lower bound on how fast you can decide statements! We explain what this means and how it comes to be.
Негізгі бет Presburger Arithmetic
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