Degrees of Relative Provability
نویسندگان
چکیده
منابع مشابه
On the Structure of the Degrees of Relative Provability
We investigate the structure of the degrees of provability, which measure the proof-theoretic strength of statements asserting the totality of given computable functions. The degrees of provability can also be seen as an extension of the investigation of relative consistency statements for firstorder arithmetic (which can be viewed as Π1-statements, whereas statements of totality of computable ...
متن کاملHonest elementary degrees and degrees of relative provability without the cupping property
An element a of a lattice cups to an element b > a if there is a c < b such that a∪c = b. An element of a lattice has the cupping property if it cups to every element above it. We prove that there are non-zero honest elementary degrees that do not have the cupping property, which answers a question of Kristiansen, Schlage-Puchta, and Weiermann [17]. In fact, we show that if b is a sufficiently ...
متن کاملFinite groups with three relative commutativity degrees
For a finite group $G$ and a subgroup $H$ of $G$, the relative commutativity degree of $H$ in $G$, denoted by $d(H,G)$, is the probability that an element of $H$ commutes with an element of $G$. Let $mathcal{D}(G)={d(H,G):Hleq G}$ be the set of all relative commutativity degrees of subgroups of $G$. It is shown that a finite group $G$ admits three relative commutativity degrees if a...
متن کاملfinite groups with three relative commutativity degrees
for a finite group $g$ and a subgroup $h$ of $g$, the relative commutativity degree of $h$ in $g$, denoted by $d(h,g)$, is the probability that an element of $h$ commutes with an element of $g$. let $mathcal{d}(g)={d(h,g):hleq g}$ be the set of all relative commutativity degrees of subgroups of $g$. it is shown that a finite group $g$ admits three relative commutativity degrees if a...
متن کاملOn relative enumerability of Turing degrees
Let d be a Turing degree, R[d] and Q[d] denote respectively classes of recursively enumerable (r.e.) and all degrees in which d is relatively enumerable. We proved in [ta] that there is a degree d containing differences of r.e.sets (briefly, d.r.e.degree) such that R[d] possess a least element m>0. Now we show the existence of a d.r.e. d such that R[d] has no a least element. We prove also that...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 2012
ISSN: 0029-4527
DOI: 10.1215/00294527-1722710