Sentence examples for each axiom from inspiring English sources

At steady state, we have produced 462 million genotypes per week for each Axiom system.

It can be shown that the basis is complete and that each axiom is independent.

If each axiom is true for I, then I is called a model of the theory.

This talk will introduce oriented matroids via the circuit, dual pair, and chirotope axiom systems, focusing on the motivations for each axiom system and the connections between them.

Instead of materializing a large number of different sub-ontologies, we propose to keep just one ontology, but equip each axiom with a label from an appropriate context lattice.

Given that each axiom is itself necessary, the theorem derived only from the axioms, is itself necessary.

Secondly, the increasing range and complexity of mathematical theories and their axiomatizations made it much less plausible to claim that each individual axiom was transparently true.

Gödel not only showed that each ZF axiom turned out true when 'set' is taken to mean 'constructible set', but also that the Axiom of Constructibility V=L stating that the class of constructible sets (L) are all the sets there are in the universe of sets (V) comes out true under this interpretation of 'set'set

Gödel used a method of 'inner models' to define a class of sets containing all ordinals and enough additional sets to prove within ZF set theory itself that each ZF axiom turns out true when 'set' is interpreted to mean 'constructible set'.

Values in this decreasing chain are a measure of the size of types in constraints that unify with each constraint head axiom: the size of each constraint in this chain is decreasing or there exists a position of a type argument in the constraint such that the type's size is decreasing.

For each large cardinal axiom Φ that has been reached by inner model theory, one has an axiom of the form V = LΦ.