Filling cages. Reverse mathematics and combinatorial principles
نویسندگان
چکیده
منابع مشابه
Reverse mathematics and well-ordering principles: A pilot study
The larger project broached here is to look at the generally Π2 sentence “ if X is well ordered then f(X) is well ordered”, where f is a standard proof theoretic function from ordinals to ordinals. It has turned out that a statement of this form is often equivalent to the existence of countable coded ω-models for a particular theory Tf whose consistency can be proved by means of a cut eliminati...
متن کاملDegrees bounding principles and universal instances in reverse mathematics
A Turing degree d bounds a principle P of reverse mathematics if every computable instance of P has a d-computable solution. P admits a universal instance if there exists a computable instance such that every solution bounds P. We prove that the stable version of the ascending descending sequence principle (SADS) as well as the stable version of the thin set theorem for pairs (STS(2)) do not ad...
متن کاملReverse-engineering Reverse Mathematics
An important open problem in Reverse Mathematics ([16, 25]) is the reduction of the first-order strength of the base theory from IΣ1 to I∆0 + exp. The system ERNA, a version of Nonstandard Analysis based on the system I∆0 + exp, provides a partial solution to this problem. Indeed, Weak König’s lemma and many of its equivalent formulations from Reverse Mathematics can be ‘pushed down’ into ERNA,...
متن کاملReverse Mathematics
In math we typically assume a set of axioms to prove a theorem. In reverse mathematics, the premise is reversed: we start with a theorem and try to determine the minimal axiomatic system required to prove the theorem (over a weak base system). This produces interesting results, as it can be shown that theorems from different fields of math such as group theory and analysis are in fact equivalen...
متن کاملCombinatorial Mathematics and Discrete Probability
Consider the experiment of tossing a 6-sided die. Suppose the outcome is 2. Does the event that the outcome is even happen? The answer is yes. Now assume that the toss produces an outcome 4, does the event that the outcome is even happen? The answer is yes. Actually observe that when the outcome is from the set {2, 4, 6}, the event happens. Thus an event in a probabilistic experiment is actuall...
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: The Bulletin of Symbolic Logic
سال: 2020
ISSN: 1079-8986,1943-5894
DOI: 10.1017/bsl.2020.39