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The relative strengths of first-order theories axiomatized by transfinite induction, for ordinals less-than ~0, and formulas restricted in quantifier complexity, is determined. This is done, in part, by describing the provably recursive functions of such theories. Upper bounds for the provably recursive functions are obtained using model-theoretic(More)
In this paper, we present the development of a W-band power amplifier (PA) circuit and a G-band low-noise amplifier (LNA) MMIC for use in a high-resolution radar system operating at 210 GHz. The power amplifier circuit has been realized using a 0.1 um InAlAs/InGaAs based depletion-type metamorphic high electron mobility transistor (MHEMT) technology in(More)
Science serves its readers as a forum for the presentation and discussion of important issues related to the advancement of science, including the presentation of minority or conflicting points of view, rather than by publishino only material on which a consenstus has been reached. Accordingly , all articles published in Science-including editorials, news(More)
Science serves its readers as a forum for the presentation and discussion of important issues related to the advance-The de ment of science, including the presentation of minority or ly condu conflicting points of view, rather than by publishing only .i. material on which a consensus has been reached. Accord-OlflOfl ingly, all articles published in(More)
The EPGY Theorem-Proving Environment is designed to help students write ordinary mathematical proofs. The system, used in a selection of computer-based proof-intensive mathematics courses, allows students to easily input mathematical expressions, apply proof strategies , verify logical inference, and apply mathematical rules. Each course has its own(More)
Science serves its readers as a forum for the pi-esentation and discussion of important issues related to the advancement of science, including the presentation of minority or conflicting points of view, rather than by publishing only material on which a consensus has been reached. Accordingly , all articles published in Science-including editorials, news(More)
We describe a model-theoretic approach to ordinal analysis via the finite com-binatorial notion of an α-large set of natural numbers. In contrast to syntactic approaches that use cut elimination, this approach involves constructing finite sets of numbers with com-binatorial properties that, in nonstandard instances, give rise to models of the theory being(More)
G-band low-noise amplifier (LNA) modules have been successfully developed for use in high-resolution radiometric imaging applications. The WR-5 waveguide modules contain a four-stage 220 GHz cascode LNA MMIC and two microstrip-to-waveguide transitions which were realized on 50 mum thick quartz substrates. The monolithic amplifier circuits were fabricated(More)