35 citations · 52 across the 6 of their papers we have counts for
7 papers
Multi-level Nonstandard Analysis and the Axiom of Choice
Karel Hrbacek
Model-theoretic frameworks for Nonstandard Analysis depend on the existence of nonprincipal ultrafilters, a strong form of the Axiom of Choice (AC). Hrbacek and Katz, APAL 72 (2021…
Effective infinitesimals in R
Karel Hrbacek, Mikhail G. Katz
We survey the effective foundations for analysis with infinitesimals developed by Hrbacek and Katz in 2021, and detail some applications. Theories SPOT and SCOT are conservative ov…
Constructing nonstandard hulls and Loeb measures in internal set theories
Karel Hrbacek, Mikhail G. Katz
Currently the two popular ways to practice Robinson's nonstandard analysis are the model-theoretic approach and the axiomatic/syntactic approach. It is sometimes claimed that the i…
Trees and Homogeneous LOTS
Ethan Akin, Karel Hrbacek
We describe those complete linearly ordered topological spaces which are homogeneous (=CHLOTS). That is, is order isomorphic with any nonempty open interval in . Using c…
Infinitesimal analysis without the Axiom of Choice
Karel Hrbacek, Mikhail G. Katz
It is often claimed that analysis with infinitesimals requires more substantial use of the Axiom of Choice than traditional elementary analysis. The claim is based on the observati…
On factoring of unlimited integers
Karel Hrbacek
A. Boudaoud asked whether every unlimited integer is a sum of a limited integer and a product of two unlimited integers. Assuming Dickson's Conjecture, the answer is negative. The…
Approaches to analysis with infinitesimals following Robinson, Nelson, and others
Peter Fletcher, Karel Hrbacek, Vladimir Kanovei +3
This is a survey of several approaches to the framework for working with infinitesimals and infinite numbers, originally developed by Abraham Robinson in the 1960s, and their const…