Kanamori–McAloon theorem
Encyclopedia
In mathematical logic
, the Kanamori–McAloon theorem, due to , gives an example of an incompleteness in Peano arithmetic, similar to that of the Paris–Harrington theorem
.
They showed that a certain finitistic special case of a theorem in Ramsey theory
due to Erdős
and Rado
is not provable in Peano arithmetic.
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
, the Kanamori–McAloon theorem, due to , gives an example of an incompleteness in Peano arithmetic, similar to that of the Paris–Harrington theorem
Paris–Harrington theorem
In mathematical logic, the Paris–Harrington theorem states that a certain combinatorial principle in Ramsey theory is true, but not provable in Peano arithmetic...
.
They showed that a certain finitistic special case of a theorem in Ramsey theory
Ramsey theory
Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that studies the conditions under which order must appear...
due to Erdős
Paul Erdos
Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...
and Rado
Richard Rado
Richard Rado FRS was a Jewish German mathematician. He earned two Ph.D.s: in 1933 from the University of Berlin, and in 1935 from the University of Cambridge. He was interviewed in Berlin by Lord Cherwell for a scholarship given by the chemist Sir Robert Mond which provided financial support to...
is not provable in Peano arithmetic.