Abstract
IntroductionThe aim of this paper is to prove the following result.Main Theorem. The Open Colouring Axiom implies that the measure algebracannot be embedded into the Boolean algebra P(N)/fin.By ‘the measure algebra’ we mean the quotient of the σ-algebra of Borel sets ofthe real line by the ideal of sets of measure zero.There are various reasons, besides sheer curiosity, why it is of interest to knowwhether the measure algebra can be embedded into P(N)/fin. One reason is thatthere is great interest in determining what the subalgebras of P(N)/fin are. Oneof the earliest and most influential result in this direction is Paroviˇcenko’s theoremfrom [11], which states that every Boolean algebra of size ℵ
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
