Title of Submission
Formally Verifying the Consistency of Arithmetic
Degree Program
Mathematics, MS
Major Advisor Name
Randall Holmes
Type of Submission
Scholarly Poster
Abstract
From the very dawn of their field, mathematical logicians have historically studied the consistency of mathematics, particularly the problem of proving the consistency of Peano arithmetic (PA). In 1930, Gödel's 2nd incompleteness theorem quickly became regarded as having shown this goal impossible, yet in 1936, Gentzen’s consistency proof gave a surprising but controversial counterpoint. Our work here is concerned with implementing a version of Gentzen’s proof in Coq, an interactive theorem prover. This will show that the consistency of arithmetic is computer verified, if one accepts Gentzen's mathematical assumptions.
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