We consider sets without subsets of higher $m$- and $tt$-degree, that we call $m$-introimmune and $tt$-introimmune sets respectively. We study how they are distributed in partially ordered degree structures. We show that: egin{itemize} item each computably enumerable weak truth-table degree contains $m$-introimmune $Pi^0_1$-sets; item each hyperimmune degree contains bi-$m$-introimmune sets. end{itemize} Finally, from known results we establish that each degree {f a} with ${f a}'geq {f 0}''$ covers a degree containing $tt$-introimmune sets.

Degrees of sets having no subsets of higher m- and tt-degree

Cintioli, P
2021-01-01

Abstract

We consider sets without subsets of higher $m$- and $tt$-degree, that we call $m$-introimmune and $tt$-introimmune sets respectively. We study how they are distributed in partially ordered degree structures. We show that: egin{itemize} item each computably enumerable weak truth-table degree contains $m$-introimmune $Pi^0_1$-sets; item each hyperimmune degree contains bi-$m$-introimmune sets. end{itemize} Finally, from known results we establish that each degree {f a} with ${f a}'geq {f 0}''$ covers a degree containing $tt$-introimmune sets.
2021
262
File in questo prodotto:
File Dimensione Formato  
COM200296.pdf

solo gestori di archivio

Descrizione: Copia autore
Tipologia: Versione Editoriale
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 359.75 kB
Formato Adobe PDF
359.75 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: https://hdl.handle.net/11581/453160
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact