A New Computation of the σ-Ordinal of KPω

نویسنده

Fernando Ferreira

چکیده

We define a functional interpretation of KPω using Howard’s primitive recursive tree functionals of finite type and associated terms. We prove that the Σ-ordinal of KPω is the least ordinal not given by a closed term of the ground type of the trees (the Bachmann-Howard ordinal). We also extend KPω to a second-order theory with ∆1-comprehension and strict-Π 1 1 reflection and show that the Σ-ordinal of this theory is still the Bachmann-Howard ordinal. It is also argued that the second-order theory is Σ1-conservative over KPω. §

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

New phase II control chart for monitoring ordinal contingency table based processes

In some statistical process monitoring applications, quality of a process or product is described by more than one ordinal factors called ordinal multivariate process. To show the relationship between these factors, an ordinal contingency table is used and modeled with ordinal log-linear model. In this paper, a new control charts based on ordinal-normal statistic is developed to monitor the ord...

متن کامل

On Generalized Weak Structures

Avila and Molina [1] introduced the notion of generalized weak structures which naturally generalize minimal structures, generalized topologies and weak structures and the structures α(g),π(g),σ(g) and β(g). This work is a further investigation of generalized weak structures due to Avila and Molina. Further we introduce the structures ro(g) and rc(g) and study the properties of the structures r...

متن کامل

Characteristics of discrete transfinite time Turing machine models: Halting times, stabilization times, and Normal Form theorems

We give an account of the basic determinants of the courses of computation of an Infinite Time Turing machine (ITTM), a model of computation which allows for transfinitely many steps of computation. One such basic theorem relates the ordinal codes capable of being output on halting computations to those capable of being produced eventually by some non-terminating computation. This socaled “λ-ζ-...

متن کامل

Classical and Effective Descriptive Complexities of ω-Powers

We prove that, for each countable ordinal ξ ≥ 1, there exist some Σ0ξ-complete ω-powers, and some Π0ξ-complete ω-powers, extending previous works on the topological complexity of ω-powers [Fin01, Fin03, Fin04, Lec01, Lec05, DF06]. We prove effective versions of these results; in particular, for each recursive ordinal ξ < ω 1 there exist some recursive sets A ⊆ 2 such that A∞ ∈ Π 0ξ \Σ 0 ξ (resp...

متن کامل