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insert connecting words to decrease humorous ambiguity
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Ryan Reich
Ryan Reich
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In 1965 Shepherdson proved that FLT is independent of the fragment of PA that uses only open induction and signature $0,S,+\times$. Indeed $2x+1\neq 2y$ is independent of that fragment. Schmerl gives a good general criterion for independence from that fragment in ``Diophantine equations in a fragment of number theory'' in the book Computation and Proof Theory, Springer Lecture Notes in Mathematics Volume 1104, 1984, pp 389-398.

Is FLT currently known to be independent of any larger fragment of PA?

In 1965 Shepherdson proved FLT independent of the fragment of PA that uses only open induction and signature $0,S,+\times$. Indeed $2x+1\neq 2y$ is independent of that fragment. Schmerl gives a good general criterion for independence from that fragment in ``Diophantine equations in a fragment of number theory'' in the book Computation and Proof Theory, Springer Lecture Notes in Mathematics Volume 1104, 1984, pp 389-398.

Is FLT currently known to be independent of any larger fragment of PA?

In 1965 Shepherdson proved that FLT is independent of the fragment of PA that uses only open induction and signature $0,S,+\times$. Indeed $2x+1\neq 2y$ is independent of that fragment. Schmerl gives a good general criterion for independence from that fragment in ``Diophantine equations in a fragment of number theory'' in the book Computation and Proof Theory, Springer Lecture Notes in Mathematics Volume 1104, 1984, pp 389-398.

Is FLT currently known to be independent of any larger fragment of PA?

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Colin McLarty
Colin McLarty
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Does any lower bound on proofs of FLT improve Shepherdson 1965?

In 1965 Shepherdson proved FLT independent of the fragment of PA that uses only open induction and signature $0,S,+\times$. Indeed $2x+1\neq 2y$ is independent of that fragment. Schmerl gives a good general criterion for independence from that fragment in ``Diophantine equations in a fragment of number theory'' in the book Computation and Proof Theory, Springer Lecture Notes in Mathematics Volume 1104, 1984, pp 389-398.

Is FLT currently known to be independent of any larger fragment of PA?