We study the Medvedev degrees of mass problems with distinguished topological properties, such as denseness, closedness, or discreteness. We investigate the sublattices generated by these degrees; the prime ideal generated by the dense degrees and its complement, a prime filter; the filter generated by the nonzero closed degrees and the filter generated by the nonzero discrete degrees. We give a complete picture of the relationships of inclusion holding between these sublattices, these filters, and this ideal. We show that the sublattice of the closed Medvedev degrees is not a Brouwer algebra. We investigate the dense degrees of mass problems that are closed under Turing equivalence, and we prove that the dense degrees form an automorphism base for the Medvedev lattice. The results hold for both the Medvedev lattice on the Baire space and the Medvedev lattice on the Cantor space.

Lewis, A.E.M., Shore, R.A., & Sorbi, A. (2011). Topological aspects of the Medvedev lattice. ARCHIVE FOR MATHEMATICAL LOGIC, 50(3-4), 319-340 [10.1007/s00153-010-0215-6].

Topological aspects of the Medvedev lattice

SORBI, ANDREA
2011

Abstract

We study the Medvedev degrees of mass problems with distinguished topological properties, such as denseness, closedness, or discreteness. We investigate the sublattices generated by these degrees; the prime ideal generated by the dense degrees and its complement, a prime filter; the filter generated by the nonzero closed degrees and the filter generated by the nonzero discrete degrees. We give a complete picture of the relationships of inclusion holding between these sublattices, these filters, and this ideal. We show that the sublattice of the closed Medvedev degrees is not a Brouwer algebra. We investigate the dense degrees of mass problems that are closed under Turing equivalence, and we prove that the dense degrees form an automorphism base for the Medvedev lattice. The results hold for both the Medvedev lattice on the Baire space and the Medvedev lattice on the Cantor space.
Lewis, A.E.M., Shore, R.A., & Sorbi, A. (2011). Topological aspects of the Medvedev lattice. ARCHIVE FOR MATHEMATICAL LOGIC, 50(3-4), 319-340 [10.1007/s00153-010-0215-6].
File in questo prodotto:
File Dimensione Formato  
lew-sho-sor.pdf

non disponibili

Descrizione: Articolo unico
Tipologia: PDF editoriale
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 266.04 kB
Formato Adobe PDF
266.04 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/22762