The countable versus uncountable branching recurrences in computability logic

Abstract

This paper introduces a new simplified version of the countable branching recurrence of Computability Logic, proves its equivalence to the old one, and shows that the basic logic induced by it is a proper superset of the basic logic induced by the uncountable branching recurrence. A further result of this paper is showing that the countable branching recurrence is strictly weaker than the uncountable branching recurrence in the sense that the latter logically implies the former but not vice versa.