Discrete Transfinite Computation

Characteristics of discrete transfinite time Turing machine models: Halting times, stabilization times, and Normal Form theorems

We give an account of the basic determinants of the courses of computation of an Infinite Time Turing machine (ITTM), a model of computation which allows for transfinitely many steps of computation. One such basic theorem relates the ordinal codes capable of being output on halting computations to those capable of being produced eventually by some non-terminating computation. This socaled “λ-ζ-...

Determinacy and Π 11 transfinite recursion along ω

It is known that almost all important set existence axioms in second order arithmetic can be characterized by determinacy schemes of infinite games. In this article, we sketch the proof of the equivalence between Π1 transfinite recursion along ω and determinacy scheme.

Infinite Time Cellular Automata: a Real Computation Model

We define a new transfinite time model of computation, infinite time cellular automata. The model is shown to be as powerful than infinite time Turing machines, both on finite and infinite inputs; thus inheriting many of its properties. We then show how to simulate the canonical real computation model, BSS machines, with infinite time cellular automata in exactly ω steps.

Some Transfinite Generalisations of Gödel's Incompleteness Theorem

Bounds on the Nodal Statuses of Some Transfinite Graphs

The bounds on the statuses of the nodes in a finite graph established by Entringer, Jackson, and Snyder are extended herein so that they apply to the statuses of the nodes in transfinite graphs of a certain kind.