منابع مشابه
The Recursion Theorem (final)
Kleene’s Recursion Theorem, though provable in only a few lines, is fundamental to computability theory and allows strong self-reference in proofs. It is a fixed-point theorem in the sense that it asserts for any total computable function f , there is a number n such that n and f(n) index (or code) the same partial computable function (though we need not have f(n) = n). In this paper we will pr...
متن کاملGeneralizations of Hedberg's Theorem
As the groupoid interpretation by Hofmann and Streicher shows, uniqueness of identity proofs (UIP) is not provable. Generalizing a theorem by Hedberg, we give new characterizations of types that satisfy UIP. It turns out to be natural in this context to consider constant endofunctions. For such a function, we can look at the type of its fixed points. We show that this type has at most one eleme...
متن کاملFrom Simplest Recursion to the Recursion of Generalizations of Cross Polytope Numbers
My research project involves investigations in the mathematical field of combinatorics. The research study will be based on the results of Professors Steven Edwards and William Griffiths, who recently found a new formula for the cross-polytope numbers. My topic will be focused on ”Generalizations of cross-polytope numbers”. It will include the proofs of the combinatorics results in Dr. Edwards ...
متن کاملGeneralizations of Wei's Duality Theorem
Wei’s celebrated Duality Theorem is generalized in several ways, expressed as duality theorems for linear codes over division rings and, more generally, duality theorems for matroids. These results are further generalized, resulting in two Wei-type duality theorems for new combinatorial structures that are introduced and named demi-matroids. These generalize matroids and are the appropriate com...
متن کاملApplications and Generalizations of the Approximation Theorem
In its basic form, the approximation theorem referred to provides simple n n combinatorial models for spaces ~ E X, where X is a connected based space. The first such result was given by James [26], who showed that ~EX is equivalent to the James construction MX. The unpublished preprint form of Dyer and gashof's paper [25] gave an approximation to QX = lira ~nEnx, and Milgram [41] gave a cellul...
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: The Journal of Symbolic Logic
سال: 2018
ISSN: 0022-4812,1943-5886
DOI: 10.1017/jsl.2018.52