Results 291 to 300 of about 49,413 (326)
Some of the next articles are maybe not open access.
The independence of “Huntington’s axioms” for boolean algebra
The Mathematical Gazette, 1978Among the various logically equivalent sets of axioms for boolean algebra ([1] discusses four of them), that referred to in the title of this article is popular because of its symmetry (self-duality) and convenience in application. The textbook presentation is essentially as follows; the qualifiers ‘left’, ‘right’ are often omitted, although the ...
openaire +1 more source
On the independence of the axioms of definiteness (Axiome der Bestimmtheit)
Journal of Symbolic Logic, 1939The question of the independence of the axioms of the theory of sets has been dealt with in a number of works, although not in a final manner. The writer will be concerned solely with the axiomatic system of Zermelo and Fraenkel, and only with that feature of the system whereby all the objects of the underlying domain are sets (so that there is no ...
openaire +2 more sources
The Independence of Axioms of B. Russell's Logical System of Axioms
2006 World Automation Congress, 2006By using the method of indeterminate coefficients, we can examine the independence of each axiom of a system of axioms. In this paper, we treat the Russell's classical logical system of axioms. We examine whether each axiom is independent or not from the other axioms and show the results.
openaire +1 more source
Complete ignorance and independence axiom: Optimism, pessimism, indecisiveness
Mathematical Social Sciences, 1986This paper studies the compatibility between a group of axioms characterizing rational behavior under complete ignorance and Savage's independence axiom. The axioms of complete ignorance include symmetry with respect to events, dominance and transitivity of strict preferences - possibly a very partial ordering of the choices, incomparabilities being ...
openaire +2 more sources
The independence of Quine's axioms *200 and *201
Journal of Symbolic Logic, 1941We refer to the axioms in Quine's book, Mathematical logic, New York, 1940.To prove the independence of *200, give xϵ α the truth value F in all cases and give (x)ϕ the same truth value as ϕ. Then clearly all formulas derivable from the other axioms besides *200 have the value T, whereas from *200 one can derive (∃x)(∃α)(xϵ α) which has the value F ...
openaire +2 more sources
Independent axiom schemata for von wright's M
Journal of Symbolic Logic, 1957In this paper we show how a modification of results due to Simons ([6]) yields a set of independent axiom schemata for von Wright's M ([8], p. 85), with a single primitive rule of inference. We first describe a system M*, then show its equivalence with M, and finally show that our schemata are independent.1. Axiomatization ofM*. We adopt the notational
openaire +2 more sources
Absolutely Independent Group Axioms
The American Mathematical Monthly, 1965R. A. Jacobson, K. L. Yocom
openaire +1 more source
The Independence Axiom Versus the Reduction Axiom: Must We Have Both?
1992Since the early 18th Century, expected utility theory became the leading theory in explaining behavior of decision makers under uncertainty. For most of this time it was used as a purely descriptive theory. For example, Ramsey (1931) explicitly assumed that people evaluate a risky prospect by its expected utility.
openaire +1 more source
A Set of Independent Axioms for Extensive Quantities
1969The modern viewpoint on quantities goes back at least to Newton’s Universal Arithmetick. Newton asserts that the relation between any two quantities of the same kind can be expressed by a real, positive number.2 In 1901, O. Hoelder gave a set of ‘Axiome der Quantitaet’, which are sufficient to establish an isomorphism between any realization of his ...
openaire +2 more sources