On the consistency strength of the Milner-Sauer conjecture
نویسنده
چکیده
1 Definitions Definition. Suppose P, ≤≤ is a poset. A ⊆ P is said to be cofinal in P iff for each x ∈ P there exists y ∈ A such that x ≤ y.
منابع مشابه
Aspects of singular cofinality
We study properties of closure operators of singular cofinality, and introduce several ZFC sufficient and equivalent conditions for the existence of antichain sequences in posets of singular cofinality. We also notice that the Proper Forcing Axiom implies the Milner-Sauer conjecture.
متن کاملThe Strength of Projective Martin Conjecture
We show that Martin’s conjecture on Π1-functions uniformly ≤T -order preserving on a cone implies Π1 Turing Determinacy over ZF+DC. In addition, it is also proved that for n ≥ 0, this conjecture for uniformly degree invariant Π2n+1functions is equivalent over ZFC to Σ2n+2-Axiom of Determinacy. As a corollary, the consistency of the conjecture for Π1-uniformly degree invariant functions implies ...
متن کاملOn the strength of PFA I∗†
Building on the work of Schimmerling ([11]) and Steel ([17]), we show that the failure of square principle at a singular strong limit cardinal implies that there is a non-tame mouse. This is the first step towards getting a model of ADR + “Θ is regular” from PFA via the core model induction. One of the wholly grails of inner model program has been determining the exact consistency strength of f...
متن کاملOn the oriented perfect path double cover conjecture
An oriented perfect path double cover (OPPDC) of a graph $G$ is a collection of directed paths in the symmetric orientation $G_s$ of $G$ such that each arc of $G_s$ lies in exactly one of the paths and each vertex of $G$ appears just once as a beginning and just once as an end of a path. Maxov{'a} and Ne{v{s}}et{v{r}}il (Discrete Math. 276 (2004) 287-294) conjectured that ...
متن کاملA note on Fouquet-Vanherpe’s question and Fulkerson conjecture
The excessive index of a bridgeless cubic graph $G$ is the least integer $k$, such that $G$ can be covered by $k$ perfect matchings. An equivalent form of Fulkerson conjecture (due to Berge) is that every bridgeless cubic graph has excessive index at most five. Clearly, Petersen graph is a cyclically 4-edge-connected snark with excessive index at least 5, so Fouquet and Vanherpe as...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Ann. Pure Appl. Logic
دوره 140 شماره
صفحات -
تاریخ انتشار 2006