A theory of ordinal numbers with Ackermann's schema

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

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

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Sequences of Ordinal Numbers

In the first part of the article we introduce the following operations: On X that yields the set of all ordinals which belong to the set X, Lim X that yields the set of all limit ordinals which belong to X, and inf X and sup X that yield the minimal ordinal belonging to X and the minimal ordinal greater than all ordinals belonging to X, respectively. The second part of the article starts with s...

متن کامل

The Ordinal Numbers

In the beginning of article we show some consequences of the regularity axiom. In the second part we introduce the successor of a set and the notions of transitivity and connectedness wrt membership relation. Then we define ordinal numbers as transitive and connected sets, and we prove some theorems of them and of their sets. Lastly we introduce the concept of a transfinite sequence and we show...

متن کامل

Cardinal and Ordinal Numbers

This paper will present a brief set-theoretic construction of the natural numbers before discussing in detail the ordinal and cardinal numbers. It will then investigate the relationship between the two proper classes, in particular the similar difficulties in discussing the size of the classes. We will end with a short section on the cardinalities of well-known infinite sets with which the read...

متن کامل

Ordinal Operations on Surreal Numbers

An open problem posed by John H. Conway in [2] was whether one could, on his system of numbers and games, ' . . . define operations of addition and multiplication which will restrict on the ordinals to give their usual operations'. Such a definition for addition was later given in [4], and this paper will show that a definition also exists for multiplication. An ordinal exponentiation operation...

متن کامل

Ordinal Numbers and the Hilbert Basis Theorem

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected].. Association for Symbolic Logic is collaborating with JSTO...

متن کامل

ذخیره 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: Journal of the Mathematical Society of Japan

سال: 1978

ISSN: 0025-5645

DOI: 10.2969/jmsj/03030413