Where can we really prove instances of the Paris-Harrington principle?
نویسندگان
چکیده
منابع مشابه
The Paris-Harrington Theorem
In Ramsey theory, very large numbers and fast-growing functions are more of a rule than an exception. The classical Ramsey numbers R(n,m) are known to be of exponential size: the original proof directly gives the upper bound R(n,m) ≤ ( m+n−2 n−1 ) , and an exponential lower bound is also known. For the van der Waerden numbers, the original proof produced upper bounds that were not even primitiv...
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We give a combinatorial proof of a tight relationship between the Kanamori-McAloon principle and the Paris-Harrington theorem with a number-theoretic parameter function. We show that the provability of the parametrised version of the Kanamori-McAloon principle can exactly correspond to the relationship between Peano Arithmetic and the ordinal ε0 which stands for the proof-theoretic strength of ...
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ژورنال
عنوان ژورنال: PAMM
سال: 2016
ISSN: 1617-7061
DOI: 10.1002/pamm.201610440