- On the structure of the Medvedev lattice
- Journal of Symbolic Logic
- Volume | Issue number
- 73 | 2
- Pages (from-to)
- Document type
- Interfacultary Research Institutes
- Institute for Logic, Language and Computation (ILLC)
We investigate the structure of the Medvedev lattice as a partial order. We prove that every interval in the lattice is either finite, in which case it is isomorphic to a finite Boolean algebra, or contains an antichain of size 2^2^\aleph_0, the size of the lattice itself. We also prove that it is consistent that the lattice has chains of this size, and in fact that these big chains occur in every interval that has a big antichain. We also study embeddings of lattices and algebras. We show that large Boolean algebras can be embedded into the Medvedev lattice as upper semilattices, but that a Boolean algebra can be embedded as a lattice only if it is countable. Finally we discuss which of these results hold for the closely related Muchnik lattice.
- go to publisher's site
If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library, or send a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.