Open AccessModels of true arithmetic are integer parts of models of real exponentation
Author(s) -
Merlin Carl,
Lothar Sebastian Krapp
Publication year - 2021
Publication title -
journal of logic and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.278
H-Index - 4
ISSN - 1759-9008
DOI - 10.4115/jla.2021.13.3
Subject(s) - exponentiation , mathematics , integer (computer science) , peano axioms , arithmetic , isomorphism (crystallography) , diophantine equation , multiplicative function , multiplicative group , real number , second order arithmetic , arithmetic progression , field (mathematics) , discrete mathematics , additive group , pure mathematics , group (periodic table) , mathematical analysis , chemistry , organic chemistry , computer science , crystal structure , crystallography , programming language
Exploring further the connection between exponentiation on real closed fields and the existence of an integer part modelling strong fragments of arithmetic, we demonstrate that each model of true arithmetic is an integer part of an exponential real closed field that is elementarily equivalent to the real numbers with exponentiation and that each model of Peano arithmetic is an integer part of a real closed field that admits an isomorphism between its ordered additive and its ordered multiplicative group of positive elements. Under the assumption of Schanuel’s Conjecture, we obtain further strengthenings for the last statement.