Lowness for integer-valued randomness

Article type: Research Article

Authors: Herbert, Ian

Affiliations: Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Rd., Singapore 119076, Singapore. iherbert@nus.edu.sg. http://www.math.nus.edu.sg/~mathir/

Abstract: A real is called integer-valued random if no integer-valued martingale can win arbitrarily much capital betting against it. A real, A, is low for integer-valued randomness if no integer-valued martingale recursive in A can succeed on an integer-valued random real. We show that lowness for integer-valued randomness coincides with recursiveness, as is the case for computable randomness.

Keywords: Algorithmic randomness, integer-valued martingales

DOI: 10.3233/COM-150045

Journal: Computability, vol. 5, no. 2, pp. 103-109, 2016