Relativistic Computers and Transfinite Computation
(1) Simple models in Malament-Hogarth spacetimes, up to \(\Delta^1_1\) or HYP.
(2) Ordinal Time Register Machines: up to \(\Pi^1_1\)- Open image in new window .
(3) Infinite Time Turing Machines: up to \(\Pi^1_2\)- Open image in new window Det(\(\Sigma^0_2)\) and beyond.
In this paper we survey some of the complexity issues surrounding discrete models of transfinite recursion. We emphasise today the connections with Proof Theory, Reverse Mathematics, and Subsystems of Second Order Number Theory as set forth in Simpson’s . Our concerns are thus mainly the logico-mathematical ones of analysing such models rather ‘implementational concerns’ (to put it broadly).
KeywordsTuring Machine Path Tree Limit Stage Ordinal Rank Reverse Mathematic
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