id	author	title	date	pages	extension	mime	words	sentences	flesch	summary	cache	txt
work_eju5e7k46je2xpw4qt5wkl3mgi	R. L. GOODSTEIN	THE SIGNIFICANCE OF INCOMPLETENESS THEOREMS	1963	13	.pdf	application/pdf	5351	317	66	number, so that in defiance of Cantor's theorem, the set of subsets is result is to say that Lowenheim's theorem for any particular formalisation of set theory is not provable by means of the resources of that logic, Godel's Theorem that all sufficiently rich formal systems necessarily contain sentences which are neither provable nor refutable in the is true that the particular undecidable sentence constructed in the proof The undecidable sentence in this Theorem of Godel has the form (yx) V(x); the number of an axiom ' is expressed by a primitive recursive relation ' n is the number of a one variable primitive recursive function ', ' n the relation which says that m is the number of a proof of formula The formula F ii this incompleteness theorem itself contains a Godel's construction of an undecidable sentence in a formal system The number of the resulting formula is of course	./cache/work_eju5e7k46je2xpw4qt5wkl3mgi.pdf	./txt/work_eju5e7k46je2xpw4qt5wkl3mgi.txt