Using some ideas of Mario Pieri, in 1926 Tarski devised an original axiomatization for plane Euclidean geometry, one considerably more concise than relations.
42.
A variant of this axiomatization denies that anything is ever part of itself ( irreflexivity ) while accepting transitivity, from which antisymmetry follows automatically.
43.
Around the end of the 1940s, some economists even rushed to argue that von Neumann-Morgenstern axiomatization of expected utility had resurrected measurability.
44.
Suppes observes that von Neumann's axiomatization was modified by Bernays " in order to remain nearer to the original Zermelo system . ..
45.
This text contained the first exposition ever of first-order logic, and posed the problem of its axiomatization of set theory ( 1956 ).
46.
Call a collection of axioms G�del's First Incompleteness Theorem then tells us that there are certain consistent bodies of propositions with no recursive axiomatization.
47.
The notion of logical implication for functional dependencies admits a complete finite axiomatization, known as "'Armstrong's axioms " '.
48.
In fact adding the axiom x \ oplus x = x to the axioms defining an MV-algebra results in an axiomatization of Boolean algebras.
49.
Verifying the Robbins conjecture required proving Huntington's equation, or some other axiomatization of a Boolean algebra, as theorems of a Robbins algebra.
50.
This axiomatization is complete, meaning that every Boolean law " s " = " t " is provable in this system.
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