Abstract Set Theory

  title={Abstract Set Theory},
  author={Richard G. Cooke},
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. 

Homotopical complexity and good spaces

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

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

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


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 .

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

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


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

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

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

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.