Theory of sets

  title={Theory of sets},
  author={Nicolas Bourbaki},
The theory of sets is a theory which contains the relational signs =, ∈ and the substantific sign ⊃ (all these signs being of weight 2); in addition to the schemes S1 to S7 given in Chapter I, it contains the scheme S8, which will be introduced in no. 6, and the explicit axioms Al (no. 3.) A2 (no. 5), A3 (§ 2, no. 1), A4 (§ 5, no. 1), and A5 (Chapter III, § 6, no. 1), These explicit axioms contain no letters; in other words, the theory of sets is a theory without constants. 
Remarks on the Theory of Quasi-sets
Quasi-set theory has been proposed as a means of handling collections of indiscernible objects. Although the most direct application of the theory is quantum physics, it can be seen per se as aExpand
Set theory in first-order logic: Clauses for Gödel's axioms
A set of clauses for set theory is presented, thus developing a foundation for the expression of most theorems of mathematics in a form acceptable to a resolution-based automated theoren prover. Expand
Axiomatization and Models of Scientific Theories
Two approaches to the axiomatization of scientific theories in the context of the so called semantic approach are discussed, according to which (roughly) a theory can be seen as a class of models. Expand
Theory of Symbolic Expressions, I
  • Masahiko Sato
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
  • 1983
The purpose of this series of papers is to introduce a new domain S of symbolic expressions (s~rps, for short:, and to study finite mathematics within the framework of S, where every finitary object is a sexp, a universal domain of finitary objects. Expand
LOGIC MAY BE SIMPLE Logic, Congruence and Algebra
This paper is an attempt to clear some philosophical questions about the nature of logic by setting up a mathematical framework. The notion of congruence in logic is defined. A logical structure inExpand
An Elementary Theory of Various Categories of Spaces in Topology
In Abstract Stone Duality the topology on a space X is treated, not as an innitary lattice, but as an exponential space X . This has an associated lambda calculus, in which monadicity of theExpand
On Bourbaki’s axiomatic system for set theory
It is shown that the system of axioms for set theory is equivalent to Zermelo–Fraenkel system with the axiom of choice but without theAxiom of foundation, and some historical and epistemological remarks are made that could explain the conservative attitude of the Group. Expand
What is an Embedding? : A Problem for Category-theoretic Structuralism
This paper concerns the proper definition of embeddings in purely category-theoretical terms. It is argued that plain category theory cannot capture what, in the general case, constitutes anExpand
On the computational meaning of axioms
This paper investigates an anti-realist theory of meaning suitable for both logical and proper axioms. Unlike other anti-realist accounts such as Dummett–Prawitz verificationism, the standardExpand
Categories in Context: Historical, Foundational, and Philosophical
kinds of structured systems in terms of schematic types, as opposed to answering ‘What is (or where is!) a structure?’, then why should we be troubled by the fact that ‘[b]y themselves they [theExpand