Clans, parent sets, litters, atoms, and allowable permutations

نویسنده

  • M. Randall Holmes
چکیده

Introductory remarks: In this note I am trying to separate out another theme in my NF consistency proof, namely the basic maneuver behind the FM construction. The advantage of this approach is that it makes it clear that the properties of the system of atoms, clans and litters constructed depend to very different degrees on the insane definition of the parent sets, which in this approach is introduced rather late. There is however no circularity in this presentation: an abstract definition of systems of clans and parent sets is given, then more and more intended properties of parent sets are assumed in further arguments until the insane specification is fully revealed. I believe that it is quite clear that the partial specifications given up to that point are all realizable in well-founded ways. Also, it is possible to motivate the insane definition of the parent sets in this document, because one knows enough about the properties of systems of clans and litters at the time it is introduced to be able to see that it will have the desired effect, if it is possible.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

NF is consistent – via tangled webs with simplified coding

This is a version combining the approach of an FM interpretation of ZFA with a tangled web of cardinals with the simplified coding scheme used in the fused type structure version. It isn’t better (or, I think, worse) than the fused type structure version, but it is different. It may have the advantage of being easier to follow for people who have fought through parts of the earlier presentation...

متن کامل

Sharply $(n-2)$-transitive Sets of Permutations

Let $S_n$ be the symmetric group on the set $[n]={1, 2, ldots, n}$. For $gin S_n$ let $fix(g)$ denote the number of fixed points of $g$. A subset $S$ of $S_n$ is called $t$-emph{transitive} if for any two $t$-tuples $(x_1,x_2,ldots,x_t)$ and $(y_1,y_2,ldots ,y_t)$ of distinct elements of $[n]$, there exists $gin S$ such that $x_{i}^g=y_{i}$ for any $1leq ileq t$ and additionally $S$ is called e...

متن کامل

Permuting machines and priority queues

Machines whose sole function is to re-order their input data are considered. Every such machine defines a set of allowable input-output pairs of permutations. These sets are studied in terms of the minimal disallowed pairs (the basis). Some allowable sets with small bases are considered including the one defined by a priority queue machine. For more complex machines defined by two or more prior...

متن کامل

Nominal renaming sets ( technical report )

Nominal techniques are based on the idea of sets with a finitelysupported atoms-permutation action. In this paper we consider the idea of sets with a finitely-supported atoms-renaming action (renamings can identify atoms; permutations cannot). We show that these exhibit many of the useful qualities found in traditional nominal techniques; an elementary sets-based presentation, inductive datatyp...

متن کامل

NF consistency proof via construction of parent functions

parent function, definition be-gins, 26abstract parent function, definition com-pleted, 30allowable permutation, 28ambiguity, axiom scheme of, 13anomaly of a near litter, 34atom, irregular, 27atoms, regular, 26axiom of weak extensionality, 15axiom scheme of ambiguity, 13axioms of NF, 11axioms of TST, 8, 10 Choice false in NF, 13Choice, axiom o...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2016