#### Room 327

#### The Muchnik topos

#### Sankha S. Basu

##### IIIT, Delhi

*We study a model of intuitionistic higher-order logic which we call the*

Muchnik topos. The Muchnik topos may be defined briefly as the category of

sheaves of sets over the topological space consisting of the Turing

degrees, where the Turing cones form a base for the topology. We note that

our Muchnik topos interpretation of intuitionistic mathematics is an

extension of the well known Kolmogorov/Muchnik interpretation of

intuitionistic propositional calculus via Muchnik degrees, i.e., mass

problems under weak reducibility. Within the Muchnik topos, we introduce a

new sheaf representation of the intuitionistic real numbers, the Muchnik

reals, which are different from the Cauchy reals and the Dedekind reals.

Done