Models of true arithmetic are integer parts of nice real closed fields

Exploring further the connection between exponentiation on real closed fields and the existence of an integer part modelling strong fragments of arithmetic, we demonstrate that each model of true arithmetic is an integer part of an exponential real closed field that is elementary equivalent to the reals with exponentiation

Optimal Results on ITRM-recognizability

Exploring further the properties of ITRM-recognizable reals, we provide a detailed analysis of recognizable reals and their distribution in G\"odels constructible universe L. In particular, we show that, for unresetting infinite time register machines, the recognizable reals coincide with the computable reals and that, for ITRMs, unrecognizables are generated at every index bigger than the first limit of admissibles. We show that a real r is recognizable iff it is $\Sigma_{1}$-definable over $L_{\omega_{\omega}^{CK,r}}$, that $r\in L_{\omega_{\omega}^{CK,r}}$ for every recognizable real $r$ and that either all or no real generated over an index stage $L_{\gamma}$ are recognizable

Towards a Church-Turing-Thesis for Infinitary Computations

We consider the question whether there is an infinitary analogue of the Church-Turing-thesis. To this end, we argue that there is an intuitive notion of transfinite computability and build a canonical model, called Idealized Agent Machines ($IAM$s) of this which will turn out to be equivalent in strength to the Ordinal Turing Machines defined by P. Koepke