AFFINE LOGIC FOR CONSTRUCTIVE MATHEMATICS

Mathematical Logic : Proof Theory , Constructive Mathematics 2965 Workshop : Mathematical Logic : Proof Theory , Constructive

The workshop “Mathematical Logic: Proof Theory, Constructive Mathematics” was centered around proof-theoretic aspects of current mathematics, constructive mathematics and logical aspects of computational complexity. Mathematics Subject Classification (2000): 03Fxx. Introduction by the Organisers The workshop Mathematical Logic: Proof Theory, Constructive Mathematics was held November 6-12, 2011...

Constructive Mathematics

Constructive Logic for All

It is a commonplace in recent metaphysics that one’s logical commitments go hand in hand with one’s metaphysics. Brouwer, Heyting and Dummett have each championed the move to constructive (intuitionistic) reasoning on the grounds of anti-realism. I hope to break this close connection, to explain why a realist ought to reason constructively.

Constructive Mathematics , in

The first part of the paper introduces the varieties of modern constructive mathematics, concentrating on Bishop’s constructive mathematics (BISH). It gives a sketch of both Myhill’s axiomatic system for BISH and a constructive axiomatic development of the real line R. The second part of the paper focusses on the relation between constructive mathematics and programming, with emphasis on Martin...

Constructive mathematics without choice

What becomes of constructive constructive mathematics without the axiom of (countable) choice? Using illustrations from a variety of areas, it is argued that it becomes better. Despite the apparent unanimity among schools of constructive mathematics with respect to the acceptance of the countable axiom of choice, I believe it to be one of the central problems, or mysteries, of constructive math...