The countable versus uncountable branching recurrences in computability logic

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 (i.e., the one in the signature {¬,∧,∨,,}{¬,∧,∨,,}) is a proper superset of the basic logic induced by the uncountable branching recurrence (i.e., the one in the signature {¬,∧,∨,,}{¬,∧,∨,,}). A further result of this paper is showing that is strictly weaker than in the sense that FF logically implies FF but not vice versa.