The collaborators constructed an algorithm to state categorically with first-order theory
that certain mathematical objects held a definitive property.
Efficiently Simulating Higher-Order Arithmetic by a First-Order Theory
 Richards, B., Mooney, R.: First-order theory
Naive set theory can be formulated in various ways, for example, as a first-order theory in a language containing identity and a membership predicate [is an element of], a theory whose axioms include all instances of the (generalised) na<ve comprehension schema:
For simplicity, I will mainly consider the first form, in which we have a first-order theory with extensionality and the generalised comprehension axiom schema.
One version of the Lowenheim-Skolem theorem tells us that every consistent first-order theory
in a countable language has a countable model whose domain is a subset of the natural numbers.
Taylor's approach is basically a first-order theory and is therefore restricted to small drop deformations.
The experimental data at high capillarity numbers, up to sample deformations of the order of 5, were found to be in good agreement with Taylor's first-order theory. The theory predicts in particular that for zero interfacial tension, the drop deforms less than the sample when it has a viscosity higher than that of the matrix and more than the sample when it has a lower viscosity.
The analyst suspends the positivism (the external standing) of the first-order theory
, so to speak (e.g., balance-of-power theory), in order to make a second-order causal argument (e.g., that balance-of-power theory has helped produce the states system).
The first-order theory of operation requires that for maximum DC-to-RF conversion efficiency the DC voltage drop across the avalanche layer must be minimized compared to the drop across the drift layer, since only in the drift layer is the AC current antiphase to the AC voltage.
This first Ku-band HJ-IMPATT diode (and to some extent the first K-band HJ-IMPATT diode profile) proved vital in the development of the first-order theory of operation.
Kharlampovich developed an algorithm to state categorically with first-order theory
that certain mathematical objects (in that instance free groups) held a definitive property.