The Constructive Content of Nonstandard Measure Existence Proofs - Is There Any?
نویسندگان
چکیده
Some examples are given which cast some light on such questions as: What (if any) constructive sense can be made out of typical nonstandard measure existence results? Can NSA give any insight into constructive measure
منابع مشابه
A nonstandard proof of a lemma from constructive measure theory
The conceptual gulf between constructive analysis (in the sense of Bishop [1]) and nonstandard analysis (in the sense of Robinson [7]) is vast, despite the historical genesis of both methodologies from foundational considerations. Those who use nonstandard arguments often say of their proofs that they are “constructive modulo an ultrafilter”; implicit in this statement is the suggestion that su...
متن کاملA Neometric Survey
Nonstandard analysis is often used to prove that certain objects exist, i.e., that certain sets are not empty. In the literature one can find many existence theorems whose only known proofs use nonstandard analysis; see, for example, [AFHL]. This article will survey a new method for existence proofs, based on the concept of a neometric space. We shall state definitions and results (usually with...
متن کاملThe computational content of Nonstandard Analysis
Kohlenbach’s proof mining program deals with the extraction of effective information from typically ineffective proofs. Proof mining has its roots in Kreisel’s pioneering work on the so-called unwinding of proofs. The proof mining of classical mathematics is rather restricted in scope due to the existence of sentences without computational content which are provable from the law of excluded mid...
متن کاملNonstandard Functional Interpretations and Categorical Models
Recently, the second author, Briseid and Safarik introduced nonstandard Dialectica, a functional interpretation that is capable of eliminating instances of familiar principles of nonstandard arithmetic including overspill, underspill, and generalisations to higher types from proofs. We show that, under few metatheoretical assumptions, the properties of this interpretation are mirrored by first ...
متن کاملQuranic way of presenting proofs for God`s existence
Regardless of the view of those philosophers like Plantinga who see no need in any proof for the existence of God, scholars have presented four views on Quranic way of proving the existence of God including demonstration, awakening, implication and clear demonstration. Describing and criticizing the views in detail, the author has viewed differently. God has regarded the level of the addressee`...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999