Well-ordering principles, omega-models and Pi-1-1-comprehension

Home The Legacy of Kurt Schütte Chapter Well-ordering Principles, ω-models and -comprehension Michael Rathjen & Ian Alexander Thomson Chapter First Online: 11 August 2020 288 Accesses

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Abstract In this paper we show that over the weak theory RCA0 the existence of ω-models of -comprehension is equivalent to saying that a certain elementary endomorphism of the category of linear orders preserves well-orderings. This result continues a long line of research. Technically, among other methods, we use Schutte’s search trees and a relativized version of the ordinal analysis of -comprehension via the Ωn-rules akin to the presentation in Buchholz and Schutte’s 1988 book [3]. A crucial challenge one faces is to show that the latter approach can be made to work in a weak background theory.