Second-Order Positive Comprehension and Frege＇s Basic Law V

Richard Heck and John Burgess have shown that Frege＇s Basic Law V is consistent with predicative comprehension and that the resulting theory interprets Robinson Arithmetic. There are also many other ways to keep Frege from being contradictory. This paper shows that Basic Law V is also consistent with positive comprehension and that the resulting theory also interprets Robinson Arithmetic. In addition, the theory of positive Frege provides a new understanding of Dummett＇s ＂indefinitely extensible concepts.＂