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Arch Math Log 2021 15;60(3-4):343-411. Epub 2020 Sep 15.

Institute of Discrete Mathematics and Geometry, TU Wien, Wiedner Hauptstraße 8-10/104, 1040 Wien, Austria.

We reimplement the creature forcing construction used by Fischer et al. (Arch Math Log 56(7-8):1045-1103, 2017. 10. Read More

Arch Math Log 2021 15;60(5):525-527. Epub 2021 Jun 15.

Centro de Informática-Univ Federal de Pernambuco (UFPE), Av. Jornalista Aníbal Fernandes, s/n Cidade Universitária, 50740-560 Recife, PE Brazil.

Arch Math Log 2020 20;59(7):879-892. Epub 2020 Feb 20.

Institute of Mathematics, The Hebrew University of Jerusalem, Edmond Safra Campus Givat Ram, 9190401 Jerusalem, Israel.

We consider a version of -Miller forcing on an uncountable cardinal . We show that under this forcing collapses to and adds a -Cohen real. The same holds under the weaker assumptions that , , and forcing with collapses to . Read More

Arch Math Log 2020 13;59(7):835-864. Epub 2020 Feb 13.

Kazan Federal University, 18 Kremlyovskaya str., Kazan, Russia 420008.

Computably enumerable equivalence relations (ceers) received a lot of attention in the literature. The standard tool to classify ceers is provided by the computable reducibility . This gives rise to a rich degree structure. Read More