Constructivity as Continuity : An Approach to Constructive and Computable Mathematics without Constructive Logic
A simple universal approach for investigating constructivity computability, and computational complexity in mathematics is presented. The approach is based on a general Type 2 theory of continuity and computability and can be considered as a consequent extension of the Polish recursive analysis. lt does not require constructive logic but a certain kind of continuity can be interpreted as constructivity. This contribution outlines very shortly Type 2 theory of continuity and computability and tries to explain the character and power of the approach by simple examples. lt is claimed that for investigating constructivity and computability in mathematical theories constructive logic is dispensable.
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