In the mathematical field of set theory, Martin's axiom, introduced by Donald A. Martin and Robert M. Solovay (1970), is a statement which is independent of the usual axioms of ZFC set theory. It is implied by the continuum hypothesis, but it is consistent with ZFC and the negation of the continuum hypothesis. Informally, it says that all cardinals less than the cardinality of the continuum, c, behave roughly like . The intuition behind this can be understood by studying the proof of the Rasiowa–Sikorski lemma. It is a principle that is used to control certain forcing arguments.
Read more about Martin's Axiom: Statement of Martin's Axiom, Equivalent Forms of MA(k), Consequences
Famous quotes containing the words martin and/or axiom:
“I learned from the git-go in the joint to get in touch with the soft, nurturing side of myself, the feminine side.”
—Wesley Strick, U.S. screenwriter, and Martin Scorsese. Max Cady (Robert DeNiro)
“The writer who neglects punctuation, or mispunctuates, is liable to be misunderstood.... For the want of merely a comma, it often occurs that an axiom appears a paradox, or that a sarcasm is converted into a sermonoid.”
—Edgar Allan Poe (1809–1845)