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Nach einer kurzen Einleitung (3 1) wird in § 2 untersucht, welchen Bedingungen die Lagrangesche Funktion fi eines Systems von Feldern geniigen muss, damit Dichte und Strom der elektrischen Ladung oder ahnlicher Grossen (wie z.B. die Dichte schwerer Teilchen) einer Kontinuitatsgleichung Geniige leisten. In diesem Zusammenhang wird das Postulat der… (More)
Some basic theorems about composition and other key constructs of set theory were proved using McCune’s computer program OTTER, building on Quaife’s modification of Gödel’s class theory. Our proofs use equational definitions in terms of Gödel’s flip and rotate functors. A new way to prove the composition of homomorphisms theorem is also presented.
Some basic theorems about ordinal numbers were proved using McCune’s computer program OTTER, building on Quaife’s modification of Gödel’s class theory. Our theorems are based on Isbell’s elegant definition of ordinals. Neither the axiom of regularity nor the axiom of choice is used.
A computer implementation of Gödel’s algorithm for class formation in Mathematica was used to formulate definitions and theorems about iteration in Gödel’s class theory. The intent is to use this approach for automated reasoning about a variety of applications of iteration using McCune’s automated reasoning program Otter. The applications include the theory… (More)
The GOEDEL program is an ever-growing collection of currently more than thirty thousand rewrite rules for transforming expressions in Gödel’s class theory in the hope of thereby simplifying them. A brief survey of the program and its use is presented. A few striking results obtained recently using the program are featured to provide some of the flavor of… (More)
definition Definition. The class of all bands is defined by a class-wrapped membership rule. In:= class@t_, member@x_, BANDSDD := ReleaseHold@Module@8u = Unique@D<, class@t, and@member@x, HoldPattern@SEMIGPSDD, forall@u, implies@member@u, fix@domain@xDDD, member@pair@pair@u, uD, uD, xDDDDDDD The DownValues of class need to be sorted to put this rule… (More)
The GOEDEL program, a computer implementation of Gödel’s algorithm for class formation in Mathematica was used for formulating definitions and discovering theorems about topology and its generalizations, working within Gödel’s class theory. A general characterization of CORE[x] and HULL[x] functions discovered in the course of this work is the primary focus… (More)