# Automorphisms of the Lattice of Recursively Enumerable Sets by Peter Cholak

By Peter Cholak

This paintings explores the relationship among the lattice of recursively enumerable (r.e.) units and the r.e. Turing levels. Cholak offers a degree-theoretic approach for developing either automorphisms of the lattice of r.e. units and isomorphisms among numerous substructures of the lattice. as well as offering one other evidence of Soare's Extension Theorem, this system is used to end up a set of recent effects, together with: each non recursive r.e. set is automorphic to a excessive r.e. set; and for each non recursive r.e. set \$A\$ and for each excessive r.e. measure h there's an r.e. set \$B\$ in h such that \$A\$ and \$B\$ shape isomorphic critical filters within the lattice of r.e. units.

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L Gentzens Schulerfolg Gentzen wurde von seinen Lehrem, die sofort seine Begabung erkannten, auf das vorteilhafteste gefOrdert. Gentzen hatle ein ganzes Jahr in der Bergener Schule kein Latein gehabt. Sein Klassenkamerad und Conabiturient Burkhart Schwerin, spater Oberstudienrat in Schwerin und Hamburg, berichtet: "Er holte die erforderlichen Kenntnisse in den Sommerferien nach und setzte sich dann von Anfang an, wie in fast allen anderen Fiichem, an die Spitze der Klasse. Er wurde Primus und blieb es bis zum Abitur.

Er war sehr bescheiden und genligsam (...

10. Physik: gut 11. Chemie: 12. Biologie: 13. Zeichnen und Kunstunterricht: sehr gut 14. Musik: geniigend 15. Leibesiibungen: gut 16. Handschrift: gut. Er hat die Reifepriifung "mit Auszeichnung" bestanden. Der unterzeichnete PriifungsausschuB hat ihm demnach das Zeugnis der Reife zuerkannt. Gentzen will Mathematik studieren. Stralsund, den 29. Febr. 1928 Staatlicher PriifungsausschuB". 59 Der Logiker und Wissenschaftshistoriker Gerd Robbel (1986, a und b) vermutet einen philosophischen EinfluB von Alfons Bilharz auf die Einstellungen Gerhard Gentzens.