arXiv subjects

Robert S. Lubarsky

Publications and source records attributed to Robert S. Lubarsky.

4 recordsLinked to original sources

arXiv2019

Feedback computability on Cantor space

We introduce the notion of feedback computable functions from $2^ω$ to $2^ω$, extending feedback Turing computation in analogy with the standard notion of computability for functions from $2^ω$ to $2^ω$. We then show that the feedback computable functions are precisely the effectively Borel functions. With this as motivation we define the notion of a feedback computable function on a structure, independent of any coding of the structure as a real. We show that this notion is absolute, and as an example characterize those functions that are computable from a Gandy ordinal with some finite subset distinguished.

math.LO↗

arXiv2015

Principles Weaker than BD-N

BD-N is a weak principle of constructive analysis. Several interesting principles implied by BD-N have already been identified, namely the closure of the anti-Specker spaces under product, the Riemann Permutation Theorem, and the Cauchyness of all partially Cauchy sequences. Here these are shown to be strictly weaker than BD-N, yet not provable in set theory alone under constructive logic.

math.LO↗

arXiv2015

Realizability Models Separating Various Fan Theorems

We develop a realizability model in which the realizers are the reals not just Turing computable in a fixed real but rather the reals in a countable ideal of Turing degrees. This is then applied to prove several separation results involving variants of the Fan Theorem.

math.LO↗

arXiv2015

Separating the Fan Theorem and Its Weakenings

Varieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Some of the implications have been shown to be strict, others strict in a weak context, and yet others not at all, using disparate techniques. Here we present a family of related Kripke models which separates all of the as yet identified fan theorems.

math.LO↗