# Abstract Set Theory

@article{Cooke1954AbstractST, title={Abstract Set Theory}, author={Richard G. Cooke}, journal={Nature}, year={1954}, volume={173}, pages={967-967} }

Abstract Set TheoryBy Prof. Abraham A. Fraenkel. (Studies in Logic and the Foundations of Mathematics.) Pp. xii + 480. (Amsterdam: North-Holland Publishing Co., 1953.) 38f.; 76s.

## 44 Citations

### Homotopical complexity and good spaces

- Mathematics
- 2006

This paper is an exploration of two ideas in the study of closed classes: the A-complexity of a space X and the notion of good spaces (spaces A for which C(A) = C(A)). A variety of formulae for the…

### The development of multiset theory

- Mathematics
- 1991

The development of multiset theory is surveyed from its earliest beginnings to its most recent applications in mathematics, logic and computational mathematics.

### On the Maximality of Functors

- Mathematics
- 2015

Suppose we are given a dependent element `′. Is it possible to compute scalars? We show that u > √ 2. In [18], the main result was the derivation of ultra-arithmetic equations. T. Erdős [18] improved…

### CANTORIAN SET THEORY

- PhilosophyThe Bulletin of Symbolic Logic
- 2018

A ‘Cantorian’ system is presented which excludes empty and singleton sets, investigating the consequences of their omission, and asking whether their absence is an obstacle to the theory’s ability to represent ordered pairs or to support the arithmetization of analysis or the development of the theory of cardinals and ordinals.

### Alternative algebraic definitions of the Hessenberg natural operations in the ordinal numbers .

- Mathematics
- 1995

This paper proves prerequisite results for the theory of Ordinal Real Numbers. In this paper, is proved that any field-inherited abelian operations and the Hessenberg operations ,in the ordinal…

### On the Simplicity and Speed of Programs for Computing Infinite Sets of Natural Numbers

- MathematicsJ. ACM
- 1969

It is suggested that there are infinite computable sets of natural numbers with the property that no infinite subset can be computed more simply or more quickly than the whole set. Attempts to…

### A DEDEKIND-STYLE AXIOMATIZATION AND THE CORRESPONDING UNIVERSAL PROPERTY OF AN ORDINAL NUMBER SYSTEM

- MathematicsThe Journal of Symbolic Logic
- 2022

Abstract In this paper, we give an axiomatization of the ordinal number system, in the style of Dedekind’s axiomatization of the natural number system. The latter is based on a structure
$(N,0,s)$
…

### A straightened proof for the uncountability of R

- Mathematics
- 2010

Cantor’s proof of this result [2, §2] makes use of nested intervals, but today a proof based on another ingenious idea of Cantor is more popular, namely the diagonal method, which he introduced in…

### Constructive versions of ordinal number classes

- Mathematics
- 1961

Abstract : In article 1 we give certain terminology and background related to the classial theory of ordinals. In article 2 we discuss S1, S3 and the general notion of system of notations. In article…

### Modal logic of time division

- Computer ScienceAdvances in Modal Logic
- 2008

LTD is syntactically like basic modal logic with an additional unary operator but it has an interval-based semantics on structures with arbitrary linear frames and is translatable into weak monadic secondorder logic but not into first-order logic.