Lectures on the Hyperreals

Goldblatt, R. (1998). Lectures on the Hyperreals: An Introduction to Nonstandard Analysis. Springer.

Type

Book

Intellectual base

Textbook

Year

1998

DOI

10.1007/978-1-4612-0615-6

ISBN

9781461268413

DOI registrant

Springer Nature

Link

https://doi.org/10.1007/978-1-4612-0615-6

Cited by

5 citations across 5 artifacts.

Domain-specific

• Loeb space
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Monad (nonstandard analysis)
  • A nonstandard-analysis monad is the infinitesimal neighborhood defined by difference from a center being infinitesimal.
• Non-Archimedean Ordered Field
  • Non-Archimedean ordered-field axioms alone do not supply transfer, saturation, internal sets, or a standard-part map.
• Overspill
  • Some sources call this overflow or spillover, and some use overspill for closely related formulations, so the direction and hypotheses must be stated rather than inferred from the label.
• Standard Part Function
  • Existence uses completeness of \(\mathbb R\); uniqueness follows because two distinct reals cannot differ by an infinitesimal.

Verification

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