This paper investigates the algebraic structure of the Medvedev lattice M. We prove that M is not a Heyting algebra. We point out some relations between M and the Dyment lattice and the Mucnik lattice. Some properties of the degrees of enumerability are considered. We give also a result on embedding countable distributive lattices in the Medvedev lattice.
Sorbi, A. (1990). Some remarks on the algebraic structure of the Medvedev Lattice. THE JOURNAL OF SYMBOLIC LOGIC, 55(2), 831-853 [10.2307/2274668].
Some remarks on the algebraic structure of the Medvedev Lattice
Sorbi, Andrea
1990-01-01
Abstract
This paper investigates the algebraic structure of the Medvedev lattice M. We prove that M is not a Heyting algebra. We point out some relations between M and the Dyment lattice and the Mucnik lattice. Some properties of the degrees of enumerability are considered. We give also a result on embedding countable distributive lattices in the Medvedev lattice.
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https://hdl.handle.net/11365/1082618