Power set recursion

Power Domains Supporting Recursion and Failure

Following the program of Moggi, the semantics of a simple non-deterministic functional language with recursion and failure is described by a monad. We show that this monad cannot be any of the known power domain constructions, because they do not handle non-termination properly. Instead, a novel construction is proposed and investigated. It embodies both non-determinism (choice and failure) and...

Recursion of Set Trajectories in a Transformation Group1

The Uniform Regular Set Theorem in a-Recursion Theory

Several new features arise in the generalization of recursion theory on crl to recursion theory on admissible ordinals d, thus making ¿y-recursion theory an interesting theory. One of these is the appearance of irregular sets. A subset A of a is called regular (over a), if we have for all B<a that AnBeL-, otherwise A is called irregular (over ø). So in the special case of ordinary recursion the...

Transfinite recursion and computation in the iterative conception of set

Transfinite recursion is an essential component of set theory. In this paper, we seek intrinsically justified reasons for believing in recursion and the notions of higher computation that surround it. In doing this, we consider several kinds of recursion principles and prove results concerning their relation to one another. We then consider philosophical motivations for these formal principles ...

The Power Set Function

We survey old and recent results on the problem of finding a complete set of rules describing the behavior of the power function, i.e. the function which takes a cardinal κ to the cardinality of its power 2κ.