Author | Sikorski, Roman. author |
---|---|

Title | Boolean Algebras [electronic resource] / by Roman Sikorski |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1960 |

Edition | Second Edition |

Connect to | http://dx.doi.org/10.1007/978-3-662-01507-0 |

Descript | X, 237 p. online resource |

SUMMARY

There are two aspects to the theory of Boolean algebras; the algebraic and the set-theoretical. A Boolean algebra can be considered as a special kind of algebraic ring, or as a generalization of the set-theoretical notion of a field of sets. Fundamental theorems in both of these directions are due to M. H. STONE, whose papers have opened a new era in the developยญ ment of this theory. This work treats the set-theoretical aspect, with little mention being made of the algebraic one. The book is composed of two chapters and an appendix. Chapter I is devoted to the study of Boolean algebras from the point of view of finite Boolean operations only; a greater part of its contents can be found in the books of BIRKHOFF [2J and HERMES [IJ. Chapter II seems to be the first systematic study of Boolean algebras with infinite Boolean operations. To understand Chapters I and II it suffices only to know fundamental notions from general set theory and set-theoretical topology. No knowยญ ledge of lattice theory or of abstract algebra is presumed. Less familiar topological theorems are recalled, and only a few examples use more advanced topological means; but these may be omitted. All theorems in both chapters are given with full proofs

CONTENT

Terminology and notation -- I. Finite joins and meets -- II. Infiinite joins and meets -- Append -- ยง 39. Relation to other algebras -- ยง 40. Applications to mathematical logic. Classical calculi -- ยง 41. Topology in Boolean algebras. Applications to non-classical logic -- ยง 42. Applications to measure theory -- ยง 43. Measurable functions and real homomorphisms -- ยง 44. Measurable functions. Reduction to continuous functions -- ยง 45. Applications to functional analysis -- ยง 46. Applications to foundations of the theory of probability -- ยง 47. Problems of effectivity -- List of symbols -- Author Index

Mathematics
Mathematical logic
Functions of real variables
Mathematics
Real Functions
Mathematics general
Mathematical Logic and Formal Languages