Effective choice functions and index sets

Partial choice functions for families of finite sets

Let p be a prime. We show that ZF + “Every countable set of p-element sets has an infinite partial choice function” is not strong enough to prove that every countable set of p-element sets has a choice function, answering an open question from [1]. The independence result is obtained by way of a permutation (FraenkelMostowski) model in which the set of atoms has the structure of a vector space ...

On Pre-θ-Open Sets and Two Classes of Functions

Isomorphism Types of Index Sets of Partial Recursive Functions

1. Let [qo, qi,q2, ■ • ■ J be a Kleene enumeration of partial recursive functions. If / is such a function, denote by 9f its index set, 9f= {ra|g„^/}. Insofar as the indices of a partial recursive function correspond to the different sets of "instructions" for computing its values, it is natural to ask how much of the "complexity" of the function is reflected by its index set; for example, one ...

Variable Sets and Functions

In the paper a graph-based speciication language for semantic modeling is proposed. It is as handy as conventional graphical languages but, in contrast to them, possesses a precisely formalized semantics based on certain ideas of the mathematical category theory. In particular, it provides mathematically correct semantics for formerly somewhat mythical notions of object identity and weak entity...

Drought monitoring using deciles index standardized precipitation index and effective Drought index in tehran province iran