Paris-Harrington principles, reflection principles and transfinite induction up to ϵ0
نویسندگان
چکیده
منابع مشابه
Induction Rules, Reflection Principles, and Provably Recursive Functions
A well known result of D Leivant states that over basic Kalmar ele mentary arithmetic EA the induction schema for n formulas is equivalent to the uniform re ection principle for n formulas We show that frag ments of arithmetic axiomatized by various forms of induction rules admit a precise axiomatization in terms of re ection principles as well Thus the closure of EA under the induction rule fo...
متن کاملThe Paris-Harrington Theorem
In Ramsey theory, very large numbers and fast-growing functions are more of a rule than an exception. The classical Ramsey numbers R(n,m) are known to be of exponential size: the original proof directly gives the upper bound R(n,m) ≤ ( m+n−2 n−1 ) , and an exponential lower bound is also known. For the van der Waerden numbers, the original proof produced upper bounds that were not even primitiv...
متن کاملOn reflection principles
Gödel initiated the program of finding and justifying axioms that effect a significant reduction in incompleteness and he drew a fundamental distinction between intrinsic and extrinsic justifications. Reflection principles are the most promising candidates for new axioms that are intrinsically justified. Taking as our starting point Tait’s work on general reflection principles, we prove a serie...
متن کاملGlobal Reflection Principles
Reflection Principles are commonly thought to produce only strong axioms of infinity consistent with V = L. It would be desirable to have some notion of strong reflection to remedy this, and we have proposed Global Reflection Principles based on a somewhat Cantorian view of the universe. Such principles justify the kind of cardinals needed for, inter alia , Woodin’s Ω-Logic.1 To say that the un...
متن کاملProof Pearl: Wellfounded Induction on the Ordinals up to ε0
We discuss a proof of the wellfounded induction theorem for the ordinals up to ε0. The proof is performed on the embedding of ACL2 in HOL-4, thus providing logical justification for that embedding and supporting the claim that the ACL2 logic has a model.
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1986
ISSN: 0168-0072
DOI: 10.1016/0168-0072(86)90072-2