Arithmetical transfinite induction and hierarchies of functions
نویسنده
چکیده
We generalize to the case of arithmetical transfinite induction the following three theorems for PA: the Wainer Theorem, the Paris–Harrington Theorem, and a version of the Solovay–Ketonen Theorem. We give uniform proofs using combinatorial constructions.
منابع مشابه
On the hierarchies of universal predicates
We investigate a hierarchy of arithmetical structures obtained by transfinite addition of a canonic universal predicate, where the canonic universal predicate for M is defined as a minimum universal predicate for M in terms of definability. We determine the upper bound of the hierarchy and give a characterisation for the sets definable in the hierarchy.
متن کامل2 4 M ar 2 00 7 On the hierarchies of universal predicates
We investigate a hierarchy of arithmetical structures obtained by transfinite addition of a canonic universal predicate, where the canonic universal predicate for M is defined as a minimum universal predicate for M in terms of definability. We determine the upper bound of the hierarchy and give a characterisation for the sets definable in the hierarchy.
متن کاملA Predicative Harmonization of the Time and Provable Hierarchies
A decidable transfinite hierarchy is defined by assigning ordinals to the programs of an imperative language. It singles out: the classes TIMEF(n) and TIMEF(nc); the finite Grzegorczyk classes at and above the elementary level, and the Σk-IND fragments of PA. Limited operators, diagonalization, and majorization functions are not used.
متن کاملOn the Strength of König's Duality Theorem for Countable Bipartite Graphs
Let CKDT be the assertion that, for every countably infinite bipartite graph G, there exist a vertex covering C of G and a matching M in G such that C consists of exactly one vertex from each edge in M . (This is a theorem of Podewski and Steffens [12].) Let ATR0 be the subsystem of second order arithmetic with arithmetical transfinite recursion and restricted induction. Let RCA0 be the subsyst...
متن کاملMetapredicative Subsystems of Analysis
In this paper we present some metapredicative subsystems of analysis. We deal with reflection principles, ω-model existence axioms (limit axioms) and axioms asserting the existence of hierarchies. We show several equivalences of the introduced subsystems. In particular we prove the equivalence of Σ1 transfinite dependent choice and Π 1 2 reflection on ω-models of Σ1-DC.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008