منابع مشابه
Proving Unprovability
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We construct long sequences of braids that are descending with respect to the standard order of braids (“Dehornoy order”), and we deduce that, contrary to all usual algebraic properties of braids, certain simple combinatorial statements involving the braid order are true, but not provable in the subsystems IΣ1 or IΣ2 of the standard Peano system. It has been known for decades that there exist s...
متن کاملSeveral proofs of PA-unprovability
In this article we give unprovability proofs of several combinatorial statements using the method of indiscernibles. Our first two statements are strong versions of KM (the Kanamori-McAloon principle) and KM(2), (the Kanamori-McAloon principle for pairs) that both allow unexpectedly simple proofs. We proceed to discuss results by A.Weiermann and G.Lee on IΣkprovability/unprovability of the prin...
متن کاملUnprovability of the Logical Characterization of Bisimulation
We quickly review labelled Markov processes (LMP) and provide a counterexample showing that in general measurable spaces, event bisimilarity and state bisimilarity differ in LMP. This shows that the logic in Desharnais [3] does not characterize state bisimulation in non-analytic measurable spaces. Furthermore we show that, under current foundations of Mathematics, such logical characterization ...
متن کاملBrief Introduction to Unprovability
The article starts with a brief survey of Unprovability Theory as of summer 2006. Then, as an illustration of the subject’s model-theoretic methods, we re-prove threshold versions of unprovability results for the Paris-Harrington Principle and the Kanamori-McAloon Principle using indiscernibles. In addition, we obtain a short accessible proof of unprovability of the ParisHarrington Principle. T...
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ژورنال
عنوان ژورنال: Archive for Mathematical Logic
سال: 1993
ISSN: 0933-5846,1432-0665
DOI: 10.1007/bf01387407