In the proof of Gödel's First Incompleteness Theorem, you need to choose a way to encode formulas and proofs as numbers. The easy way to do this is to take 2^i₀3^i₁5^i₃...p_j^i_j. However you can instead use the Chinese Remainder Theorem to pick a number congruent to i₀ mod p₀, congruent to i₁ mod p₁, etc. (Of course, you need to pick big enough primes then.) The advantage of doing this is you no longer need exponentiation in your theory, just multiplication and addition.

In the proof of Gödel's First Incompleteness Theorem, you need to choose a way to encode formulas and proofs as numbers. The easy way to do this is to take 2^i₀3^i₁5^i₃...p_j^i_j. However you can instead use the Chinese Remainder Theorem to pick a number congruent to i₀ mod p₀, congruent to i₁ mod p₁, etc. (Of course, you need to pick big enough primes then.) The advantage of doing this is you no longer need exponentiation in your theory, just multiplication and addition.

In the proof of Gödel's First Incompleteness Theorem, you need to choose a way to encode formulas and proofs as numbers. The easy way to do this is to take 2^i₀3^i₁5^i₃...p_j^i_j. However you can instead use the Chinese Remainder Theorem to pick a number congruent to i₀ mod p₀, congruent to i₁ mod p₁, etc. (Of course, you need to pick big enough primes then.) The advantage of doing this is you no longer need exponentiation in your theory, just multiplication and adition.

In the proof of Gödel's First Incompleteness Theorem, you need to choose a way to encode formulas and proofs as numbers. The easy way to do this is to take 2^i₀3^i₁5^i₃...p_j^i_j. However you can instead use the Chinese Remainder Theorem to pick a number congruent to i₀ mod p₀, congruent to i₁ mod p₁, etc. (Of course, you need to pick big enough primes then.) The advantage of doing this is you no longer need exponentiation in your theory, just multiplication and addition.