Minimal partial clones
نویسندگان
چکیده
منابع مشابه
Uniqueness of minimal coverings of maximal partial clones
A partial function f on an k-element set Ek is a partial Sheffer function if every partial function on Ek is definable in terms of f . Since this holds if and only if f belongs to no maximal partial clone on Ek, a characterization of partial Sheffer functions reduces to finding families of minimal coverings of maximal partial clones on Ek. We show that for each k ≥ 2 there exists a unique minim...
متن کاملExtendable local partial clones
We investigate interpolation and extrapolation properties of composition-closed sets of partial operations defined on an infinite set E. Considering local completeness (interpolation property) the structure of a maximal local partial clone is described via its intersections with the full partial clones on every finite k-element (k 2) subset of E. The criteria are established which characterize ...
متن کاملUncountable Families of Partial Clones Containing Maximal Clones
Let A be a non singleton finite set. We show that every maximal clone determined by a prime affine or h-universal relation on A is contained in a family of partial clones on A of continuum cardinality. MSC 2000: 03B50, 08A40, 08A55
متن کاملThe Minimal Clones above the Permutations
We determine the atoms of the interval of the clone lattice consisting of those clones which contain all permutations, on an infinite base set. This is equivalent to the description of the atoms of the lattice of transformation monoids above the permutations. 1. The problem and the result Let X be an infinite set of cardinality κ = אα, let O be the set of all finitary operations on X, and for a...
متن کاملPartial Clones Containing all Boolean Monotone Self-dual Partial Functions
The study of partial clones on 2 := {0, 1} was initiated by R. V. Freivald. In his fundamental paper published in 1966, Freivald showed, among other things, that the set of all monotone partial functions and the set of all self-dual partial functions are both maximal partial clones on 2. Several papers dealing with intersections of maximal partial clones on 2 have appeared after Freivald work. ...
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: Bulletin of the Australian Mathematical Society
سال: 1991
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700029919