Various ordinal functions which in the past have been used to describe ordinals not much
larger than the Bachmann–Howard ordinal are set into relation. Special efforts are made to …

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(*) What are we implicitly committed to in accepting a theory S and what can we justifiably
accept? As is well-known,(*) has its roots in the work by Kreisel (1958), Kreisel (1970). 2 Our …

The notion of unfolding a schematic formal system was introduced by Feferman in 1996 in
order to answer the following question: Given a schematic system S, which operations and …

The purpose of this article is to present a range of theories with prooftheoretic ordinal ψ
(ΓΩ+). This ordinal parallels the ordinal of predicative analysis, Γ, and our theories are …

The philosophical problem of implicit commitment can be roughly stated in the form:(*) What
are we implicitly committed to in accepting a theory and what can we justifiably accept? As is …

Introduction In recent years a renewed interest in ordinal notations around the Bachmann-
Howard ordinal φεΩ+ 1 (0) has evolved, amongst others caused by Gerhard Jäger's …