Abstract
The Erdős–Moser theorem (EM) states that every infinite tournament has an infinite transitive subtournament. This principle plays an important role in the understanding of the computational strength of Ramsey's theorem for pairs (RT22) by providing an alternate proof of RT22 in terms of EM and the ascending descending sequence principle (ADS). In this paper, we study the computational weakness of EM and construct a standard model (ω-model) of simultaneously EM, weak König's lemma and the cohesiveness principle, which is not a model of the atomic model theorem. This separation answers a question of Hirschfeldt, Shore and Slaman, and shows that the weakness of the Erdős–Moser theorem goes beyond the separation of EM from ADS proven by Lerman, Solomon and Towsner.
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