3 papers
math.LO2021
Mathematical Incompleteness Results in First-Order Peano Arithmetic: A Revisionist View of the Early History
Saul A. Kripke
In the Handbook of Mathematical Logic, the Paris-Harrington variant of Ramsey's theorem is celebrated as the first result of a long 'search' for a purely mathematical incompletenes…
math.LO2021
The Collapse of the Hilbert Program: A Variation on the Gödelian Theme
Saul A. Kripke
The Hilbert program was actually a specific approach for proving consistency. Quantifiers were supposed to be replaced by -terms. was supposed to denote a witness to…
math.LO2020
Gödel's Theorem and Direct Self-Reference
Saul A. Kripke
In his paper on the incompleteness theorems, Gödel seemed to say that a direct way of constructing a formula that says of itself that it is unprovable might involve a faulty circul…