Due to paradoxes, this intuitive principle is not directly formalized in standard set theories.
The new picture of the program was this: Classical mathematics is to be formalized in a system which includes formalizations of all the directly verifiable (by calculation) propositions of contentual finite number theory.
Cantor's set theory (which we will not address directly here as it was not formalized) arose out of an analysis of complicated subcollections of the real line defined using tools of what we would now call topology (Cantor 1872).
The RELM/CSEP working groups formalized the LBT to test hypotheses that 'should follow directly the model, so that if the model is valid, the hypothesis should be consistent with data used in a test.
Information already captured and formalized in OWL and RDF knowledge bases can be directly utilized.
Trenchard's close co-operation with the Americans and the French was formalized when his command was redesignated the Inter-Allied Independent Air Force in late October 1918 and placed directly under Foch, the supreme commander.
An attempt to formalize the BHK semantics directly was made by Kreisel in his theory of constructions (Kreisel 1962, Kreisel 1965).
We present the following technical contributions: 1. we formalize an intrusion model directly dependent on the adversarial effort for intruding nodes and compare results for different instantiations of attack; 2.
Later, these practices were formalized through state laws during the early 1900s that allowed ballots to be mailed directly to election officials, and also gradually extended the same privileges to civilians.
IBM ibm researchers have been dabbling in the area for about seven years, doing work with agricultural genetic research companies like Monsanto.But now IBM has formalized its effort in a 50-person group, headed up by Dr. Caroline Kovac, a vice president who reports directly to Thompson.
