Notions of indifference for genericity: Union sets and subsequence sets
نویسندگان
چکیده
A set $I$ is said to be a universal indifferent for $1$-genericity if every $1$-generic $G$ and all $X \subseteq I$, $G \Delta X$ also $1$-generic. Miller showed that there no infinite $1$-genericity. We introduce two variants (union subsequence sets $1$-genericity) of the notion indifference prove are non-trivial with respect these notions. In contrast, we show non-computable weak-$1$-genericity.
منابع مشابه
Finiteness notions in fuzzy sets
Finite sets are one of the most fundamental mathematical structures. In the absence of the axiom of choice there are many different inequivalent definitions of finite even in classical logic. When we allow incomplete existence as in fuzzy sets the situation gets even more complicated. This paper gives nine distinct definitions of finite in a fuzzy context together with examples showing how the ...
متن کاملUnion-closed families of sets
A family of sets is union-closed if it contains the union of any two of its elements. Some years ago, Reimer gave a lower bound for the average size of an element of a union-closed family consisting of m sets and, two years ago, Czédli did the same under the additional condition that our sets are contained in a set with n elements. Recently Tom Eccles and I have determined the minimum average s...
متن کاملOn the Notions of Symmetry and Aperiodicity for Delone Sets
Non-periodic systems have become more important in recent years, both theoretically and practically. Their description via Delone sets requires the extension of many standard concepts of crystallography. Here, we summarise some useful notions of symmetry and aperiodicity, with special focus on the concept of the hull of a Delone set. Our aim is to contribute to a more systematic and consistent ...
متن کاملRelativizations of Randomness and Genericity Notions
A set A is a base for Schnorr randomness if it is Turing reducible to a set R which is Schnorr random relative to A, and the notion of a base for weak 1-genericity can be defined similarly. We show that A is a base for Schnorr randomness if and only if A is a base for weak 1-genericity if and only if the halting set K is not Turing reducible to A. Furthermore, we define a set A to be high for S...
متن کاملNotions of Relative Ubiquity for Invariant Sets of Relational Structures
Given a finite lexicon L of relational symbols and equality, one may view the collection of all L-structures on the set of natural numbers co as a space in several different ways. We consider it as: (i) the space of outcomes of certain infinite two-person games; (ii) a compact metric space; and (iii) a probability measure space. For each of these viewpoints, we can give a notion of relative ubi...
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: Journal of Logic and Computation
سال: 2021
ISSN: ['1465-363X', '0955-792X']
DOI: https://doi.org/10.1093/logcom/exab035