Compiling Hilbert’s operator

Hilbert’s Type Linear Operator and Some Extensions of Hilbert’s Inequality

Introduction to Bernays Text No. 6, “Appendix to Hilbert’s Lecture ‘The Foundations of Mathematics’”

Hilbert’s 1928 article, to which this piece is an appendix, was presented in July 1927 to the Hamburg Mathematical Seminar. Hilbert had first introduced his program for the foundations of mathematics in the same venue in a series of talks in 1921 (Hilbert, 1922). In the 1927 talk, he presented a mature version of his program, including technical details of the axiomatization of mathematics base...

On a more accurate half-discrete Hilbert’s inequality

* Correspondence: qlhuang@yeah. net Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, People’s Republic of China Abstract By using the way of weight coefficients and the idea of introducing parameters and by means of Hadamard’s inequality, we give a more accurate half-discrete Hilbert’s inequality with a best constant factor. We also consider its best ex...

Hilbert ’ s epsilon as an Operator of Indefinite Committed Choice

Paul Bernays and David Hilbert carefully avoided overspecification of Hilbert’s ε-operator and axiomatized only what was relevant for their proof-theoretic investigations. Semantically, this left the ε-operator underspecified. In the meanwhile, there have been several suggestions for semantics of the ε as a choice operator. After reviewing the literature on semantics of Hilbert’s epsilon operat...

Hilbert's epsilon as an operator of indefinite committed choice

Paul Bernays and David Hilbert carefully avoided overspecification of Hilbert’s ε-operator and axiomatized only what was relevant for their proof-theoretic investigations. Semantically, this left the ε-operator underspecified. In the meanwhile, there have been several suggestions for semantics of the ε as a choice operator. After reviewing the literature on semantics of Hilbert’s epsilon operat...