Lipschitz and Wadge binary games in second order arithmetic
نویسندگان
چکیده
We present a detailed formalization of Lipschitz and Wadge games in the context second order arithmetic we investigate logical strength determinacy, tightly related Semi-Linear Ordering principle, for first levels Hausdorff difference hierarchy Cantor space. As result, obtain characterizations WKL0 ACA0 terms these determinacy principles.
منابع مشابه
Determinacy of Wadge classes and subsystems of second order arithmetic
In this paper we study the logical strength of the determinacy of infinite binary games in terms of second order arithmetic. We define new determinacy schemata inspired by the Wadge classes of Polish spaces and show the following equivalences over the system RCA0, which consists of the axioms of discrete ordered semi-ring with exponentiation, ∆1 comprehension and Π 0 0 induction, and which is k...
متن کاملCorrigendum of “Determinacy of Wadge classes and subsystems of second order arithmetic”
for a pair (θ0(x), θ1(x)) of Π0 formulae such that, for all f ∈ {0, 1}N, ∀n(∃m > n)θ0(f [m]) if and only if ¬∀n∃m > nθ1(f [m]). We may assume that {s ∈ {0, 1}<N : θ0(s) ∧ θ1(s)} = ∅ and θ0(⟨⟩) by replacing θ0(x) with θ′ 0(x) ≡ (θ0(x) ∧ ¬θ1(x)) ∨ (x = ⟨⟩) and θ1(x) with θ′ 1(x) ≡ θ1(x) ∧ ¬θ0(x) ∧ (x ̸= ⟨⟩) if necessary. The above tree Tθ0,θ1 is well-founded, for if F were an infinite path of Tθ0,...
متن کاملCZF and Second Order Arithmetic
Constructive ZF + full Separation is shown to be equiconsistent with Second Order Arithmetic.
متن کاملSubsystems of Second Order Arithmetic Second Edition
Foundations of mathematics is the study of the most basic concepts and logical structure of mathematics, with an eye to the unity of human knowledge. Almost all of the problems studied in this book are motivated by an overriding foundational question: What are the appropriate axioms for mathematics? Through a series of case studies, these axioms are examined to prove particular theorems in core...
متن کاملSecond Order Arithmetic Means in Operator Ideals
We settle in the negative the question arising from [3] on whether equality of the second order arithmetic means of two principal ideals implies equality of their first order arithmetic means (second order equality cancellation) and we provide fairly broad sufficient conditions on one of the principal ideals for this implication to always hold true. We present also sufficient conditions for sec...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2023
ISSN: ['0168-0072', '1873-2461']
DOI: https://doi.org/10.1016/j.apal.2023.103301