By Lev Bukovský (auth.)

The speedy improvement of set idea within the final fifty years, quite often in acquiring lots of independence effects, strongly stimulated an realizing of the constitution of the genuine line. This publication is dedicated to the learn of the true line and its subsets making an allowance for the new result of set concept. every time attainable the presentation is completed with out the entire axiom of selection. because the booklet is meant to be self-contained, all important result of set conception, topology, degree conception, descriptive set idea are revisited with the aim to cast off superfluous use of an axiom of selection. The duality of degree and type is studied in a close demeanour. numerous statements touching on houses of the genuine line are proven to be undecidable in set concept. The metamathematics in the back of it's presently defined within the appendix. each one part includes a sequence of routines with extra results.