In 1963, Abraham Robinson applied his newly discovered nonstandard analysis to formal firstorder languages and developed a nonstandard logic [9] relative to the “truth” concept and structures. Since that time not a great deal of fundamental research has been attempted in this specific area with one notable exception [2]. However, when results from this discipline are utilized they have yielded ...

Elementary Recursive Nonstandard Analysis, in short ERNA, is a constructive system of nonstandard analysis with a PRA consistency proof, proposed around 1995 by Patrick Suppes and Richard Sommer. It is built on a previous system by Rolando Chuaqui and Patrick Suppes, which was recently reconsidered by Michal Rössler and Emil Jeřábek. A Π1-transfer principle has already been added to ERNA and th...

This paper provides a new proof of the consistency of the formal system presented by Chuaqui and Suppes in [2, 9). First, a simpler, yet stronger, system, called Elementary Recursive Nonstandard Analysis, ERNA, will be provided. Indeed, it will be shown that ERNA proves all of the theorems of the Chuaqui and Suppes system. Then a finitary consistency proof of ERNA dl be given; in particular, we...

This study was conducted as part of a project involving the evaluation of a new type of noise exposure monitoring paradigm. Laboratory tests were conducted to assess how "nonstandard" dosimeter microphones and microphone positions measured noise levels under different acoustical conditions (i.e., diffuse field and direct field). The data presented in this article reflect measurement differences...

We present a nonstandard hull construction for locally uniform groups in a spirit similar to Luxembourg’s construction of the nonstandard hull of a uniform space. Our nonstandard hull is a local group rather than a global group. We investigate how this construction varies as one changes the family of pseudometrics used to construct the hull. We use the nonstandard hull construction to give a no...

This paper provides a new proof of the consistency of a formal system similar to the one presented by Chuaqui and Suppes in 2, 9]. First, a simpler, yet in some respects stronger, system, called Elementary Re-cursive Nonstandard Analysis (ERNA) will be provided. Indeed, it will be shown that ERNA proves the main axioms of the Chuaqui and Sup-pes system. Then a nitary consistency proof of ERNA w...

Introduction  The P300 test requires well-defined and unique criteria, in addition to training for the examiners, for a uniform analysis of studies and to avoid variations and errors in the interpretation of measurement results. Objectives  The objective of this study is to verify whether there are differences in P300 with and without subtraction of traces of standard and nonstandard stimuli. M...